Faculty Profiles - NISHIDA Naoki

Papers - NISHIDA Naoki

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On Transforming Prioritized Multithreaded Programs into Logically Constrained Term Rewrite Systems Reviewed

Misaki Kojima and Naoki Nishida

Informal Proceedings of the 11th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2025) page： 39 - 51 2025.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

A transformation of multithreaded programs without priorities into logically constrained term rewrite systems (LCTRS, for short) has been proposed. In this paper, we extend it to prioritized threads by introducing a descending list of priorities into terms representing configurations. As a case study, we show a verification example in which a runtime-error verification method based on all-path reachability detects an assertion failure caused by the interrupt of a high-priority thread.

On Merging Constrained Rewrite Rules of Induction Hypotheses in Constrained Rewriting Induction Reviewed

Naoki Nishida and Nozomi Taira

Informal Proceedings of the 11th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2025) page： 85 - 96 2025.7

Authorship：Lead author,　Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

In proving constrained equations by rewriting induction (RI, for short), the Expand rule which is one of the main inference rules of RI makes an orientable constrained equation a constrained rewrite rule, called an IH rewrite rule, which can be used as an induction hypothesis. Such an IH rewrite rule may be applied to constrained equations in order to simplify them. The broader the scope of the application of IH rewrite rules, the greater the possibilities for proving constrained equations. In this paper, we modify the Expand rule of RI in order to make the scope of the application of the IH rewrite rule broader. To be more precise, in orienting a constrained equation as an IH rewrite rule, if there already exists an IH rewrite rule having the same left- and right-hand sides, then we disjunct the constraint of the orienting equation with the constraint of the existing IH rewrite rule; otherwise, the orienting equation is added to the set of IH rewrite rules as a new IH rewrite rule. We show that this modification does not lose the proof power of RI.

Transforming imperative programs into bisimilar logically constrained term rewrite systems via injective functions from configurations to terms Reviewed International journal

Naoki Nishida, Misaki Kojima, and Takumi Kato

Journal of Logical and Algebraic Methods in Programming Vol. 145 page： 1 - 18 2025.5

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier

To transform an imperative program into a logically constrained term rewrite system (LCTRS, for short), previous work transforms a list of statements into rewrite rules in a stepwise manner, and proves the correctness along the transformation and the big-step semantics of the program. On the other hand, the small-step semantics of a programming language consists of inference rules that define single transitions of configurations. Partial instances of such inference rules are almost the same as rewrite rules in the transformed LCTRS. In this paper, we aim at establishing a framework for simpler definitions and correctness proofs of transformations from programs into LCTRSs. To this end, for the transformation in previous work as an example, we show the existence of an injective function from configurations of a given program to terms, and reformulate the transformation by means of the injective function. The injective function enables us to make a one-to-one correspondence between single small-step transitions and reduction steps, and provides bisimilarity between the program and transformed LCTRS, resulting in a simpler correctness proof.

DOI： 10.1016/j.jlamp.2025.101056

A nesting-preserving transformation of SIMP programs into logically constrained term rewrite systems Reviewed International journal

Naoki Nishida, Misaki Kojima, and Ayuka Matsumi

Journal of Logical and Algebraic Methods in Programming Vol. 144 page： 1 - 15 2025.3

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier

In the last decade, several transformations of an imperative program into a logically constrained term rewrite system (LCTRS, for short) have been investigated and extended. They do not preserve the nesting of statements, generating rewrite rules like transition systems, while function calls are represented by the nesting of function symbols. Structural features of the original program must often be useful in analyzing the transformed LCTRS. To use such features, we have to know how to transform the program into the LCTRS by keeping the correspondence between statements in the program and the introduced auxiliary function symbols in the LCTRS, or by transforming the LCTRS into a control flow graph to, e.g., recover loop information. In this paper, we propose a nesting-preserving transformation of a SIMP program (a C-like integer program) into an LCTRS. The transformation is mostly based on previous work and introduces the nesting of function symbols that correspond to the nesting of statements in the original program. To be more precise, we propose a construction of a tree homomorphism which is used as a post-process of the transformation in previous work, i.e., which is applied to the LCTRS obtained from the program. As a correctness statement for the nesting-preserving transformation, we show that the tree homomorphism is sound and complete for the reduction of the LCTRS.

DOI： 10.1016/j.jlamp.2025.101045

Transforming concurrent programs with semaphores into logically constrained term rewrite systems Reviewed International journal

Misaki Kojima, Naoki Nishida, Yutaka Matsubara

Journal of Logical and Algebraic Methods in Programming Vol. 143 page： 1 - 23 2025.2

Authorship：Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier

In this paper, as a first step of modeling concurrent programs by logically constrained term rewrite systems (LCTRSs, for short), we show transformations of concurrent programs with semaphore-based exclusive control into LCTRSs. To this end, we show how to encode configurations of concurrent programs with a fixed number of processes. Then, we show how to encode some well-known operations for semaphores by rewrite rules, showing two transformations of concurrent programs with semaphores into LCTRSs. We adopt list-using and list-free approaches to the encoding of waiting queues for semaphores in LCTRSs. While the former straightforwardly uses lists, the latter uses a so-called take-a-number system in order to avoid using any recursive data structures for waiting queues.

DOI： 10.1016/j.jlamp.2024.101033

On Solving All-Path Reachability Problems for Starvation Freedom of Concurrent Rewrite Systems Under Process Fairness Reviewed International journal

Misaki Kojima and Naoki Nishida

Proceedings of the 18th International Conference on Reachability Problems (RP 2024) Vol. 15050 page： 54 - 70 2024.9

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings) Publisher：Springe, Cham

Logically constrained term rewrite systems are useful models of not only sequential but also concurrent programs. We have proposed a framework to soundly reduce starvation freedom of a concurrent program to an all-path reachability problem of the corresponding logically constrained term rewrite system, where process fairness is not considered. In this paper, we show a disproof criterion for starvation freedom and then extend the framework to starvation freedom under process fairness.

DOI： 10.1007/978-3-031-72621-7_5

On completeness of decomposion of equations with disjunctive constraints on provability of constrained rewriting induction

Nozomi Taira, Naoki Nishida, and Masahiko Sakai

Record of 2024 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( H6-4 ) page： 1 2024.8

CRaris: CR checker for LCTRSs in ARI Style

Naoki Nishida and Misaki Kojima

Proceedings of the 13th International Workshop on Confluence page： 83 - 84 2024.7

On Proving Confluence of Concurrent Programs by All-Path Reachability of LCTRSs Reviewed

Misaki Kojima and Naoki Nishida

Proceedings of the 13th International Workshop on Confluence page： 2 - 8 2024.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (conference, symposium, etc.)

A logically constrained term rewrite system (LCTRS, for short) modeling a concurrent program is usually non-terminating, left-linear, and overlapping, but sometimes confluent w.r.t. an initial ground term which corresponds to an initial configuration of the program. In this paper, we show how to prove confluence of such an LCTRS w.r.t. the initial term. To be more precise, we add the rule from the initial term to a fresh constant to the LCTRS, and construct a proof tree for the all-path reachability problem from the initial term to the constant. If the directed graph obtained from the proof tree by considering it as a cyclic proof is strongly connected and each node corresponds to a single term, then all terms reachable from the initial term can be reduced back to the initial one and thus the original LCTRS is confluent w.r.t. the initial one.

CO3 (Version 2.5)

Naoki Nishida and Misaki Kojima

Proceedings of the 13th International Workshop on Confluence page： 71 - 72 2024.7

Equational Theories and Validity for Logically Constrained Term Rewriting Reviewed International coauthorship

Takahito Aoto, Naoki Nishida, and Jonas Schöpf

Proceedings of the 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2018), LIPIcs Vol. 299 page： 31:1 - 31:21 2024.7

Authorship：Lead author Language：English Publishing type：Research paper (international conference proceedings)

Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity analysis and confluence analysis for logically constrained term rewriting, these works solely focus on the syntactic side of the formalism lacking detailed investigations on semantics. In this paper, we investigate a semantic side of logically constrained term rewriting. To this end, we first define constrained equations, constrained equational theories and validity of the former based on the latter. After presenting the relationship of validity and conversion of rewriting, we then construct a sound inference system to prove validity of constrained equations in constrained equational theories. Finally, we give an algebraic semantics, which enables one to establish invalidity of constrained equations in constrained equational theories. This algebraic semantics derives a new notion of consistency for constrained equational theories.

DOI： 10.4230/LIPIcs.FSCD.2024.31

A Sufficient Condition of Logically Constrained Term Rewrite Systems for Decidability of All-path Reachability Problems with Constant Destinations Reviewed International journal

Misaki Kojima and Naoki Nishida

Journal of Information Processing Vol. 32 page： 417 - 435 2024.5

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Information Processing Society of Japan

An all-path reachability (APR, for short) problem of a logically constrained term rewrite system (LCTRS, for short) is a pair of constrained terms representing state sets. An APR problem is demonically valid if every finite execution path from any state in the first set to an irreducible state includes a state in the second set. We have proposed a framework to reduce the non-occurrence of specified error states in a transition system represented by an LCTRS to an APR problem with irreducible constant destinations. In this paper, by focusing on quasi-termination of constrained narrowing, we characterize a class of LCTRSs of which APR problems with constant destinations are decidable. Quasi-termination of a (constrained) term w.r.t. narrowing is the finiteness of the set of reachable narrowed (constrained) terms from the initial (constrained) term up to variable renaming (and equivalence of constraints). To this end, we first introduce an inference rule for disproofs to a proof system for APR problems with constant destinations and formulate (dis)proof trees of APR problems in the style of cyclic proofs. Secondly, to prove correctness of disproof trees, we adapt constrained narrowing to LCTRSs and show soundness of constrained narrowing of LCTRSs w.r.t. constrained rewriting. Thirdly, we show a sufficient condition of LCTRSs for quasi-termination of constrained narrowing starting from linear constrained terms that have no nesting of defined symbols: Rewrite rules are right-linear and nesting-free w.r.t. defined symbols, and the application of rewrite rules for (mutually) recursive defined symbols does not increase the height of resulting constrained terms of narrowing. Finally, we show that if a constrained term is quasi-terminating w.r.t. narrowing of an LCTRS over a sort-wise finite signature with a decidable theory, then the APR problem consisting of the constrained term and an irreducible constant is decidable.

DOI： 10.2197/ipsjjip.32.417

Reducing non-occurrence of specified runtime errors to all-path reachability problems of constrained rewriting Reviewed International journal

Misaki Kojima and Naoki Nishida

Journal of Logical and Algebraic Methods in Programming Vol. 135 page： 1 - 19 2023.10

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (scientific journal)

A concurrent program with semaphore-based exclusive control can be modeled by a logically constrained term rewrite system. In this paper, we first propose a framework to reduce the non-occurrence of a specified runtime error in the program to an all-path reachability problem of the transformed logically constrained term rewrite system. Here, an all-path reachability problem of the system is a pair of state sets and is demonically valid if every finite execution path starting with a state in the first set and ending with a terminating state includes a state in the second set. Then, we propose a weakened but easily-implementable variant of an existing proof system for all-path reachability problems. As a case study, we deal with the race freedom of concurrent programs with semaphore-based exclusive control.

DOI： 10.1016/j.jlamp.2023.100903

On Singleton Self-Loop Removal for Termination of LCTRSs with Bit-Vector Arithmetic Reviewed

Ayuka Mastumi, Naoki Nishida, Misaki Kojima, and Donghoon Shin

Proceedings of the 19th International Workshop on Termination page： 1 - 6 2023.8

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (conference, symposium, etc.)

As for term rewrite systems, the dependency pair (DP, for short) framework with several kinds of DP processors is useful for proving termination of logically constrained term rewrite systems (LCTRSs, for short). However, the polynomial interpretation processor is not so effective against LCTRSs with bit-vector arithmetic (BV-LCTRSs, for short). In this paper, we propose a novel DP processor for BV-LCTRSs to solve a singleton DP problem consisting of a dependency pair forming a self-loop. The processor is based on an acyclic directed graph such that the nodes are bit-vectors and any dependency chain of the problem is projected to a path of the graph. We show a sufficient condition for the existence of such an acyclic graph, and simplify it for a specific case.

DOI： 10.48550/arXiv.2307.14094

CO3 (Version 2.4)

Naoki Nishida, Misaki Kojima, and Ayuka Matsumi

Proceedings of the 12th International Workshop on Confluence page： 67 2023.8

A New Format for Rewrite Systems Reviewed International coauthorship

Takahito Aoto, Nao Hirokawa, Dohan Kim, Misaki Kojima, Aart Middeldorp, Fabian Mitterwallner, Naoki Nishida, Teppei Saito, Jonas Schöpf, Kiraku Shintani, Rene Thiemann, and Akihisa Yamada

Proceedings of the 12th International Workshop on Confluence page： 32 - 37 2023.8

On Representations of Waiting Queues for Semaphores in Logically Constrained Term Rewrite Systems Reviewed

Misaki Kojima and Naoki Nishida

Informal Proceedings of the 10th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2023) page： 1 - 6 2023.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

A transformation of concurrent programs with semaphore-based exclusive control and waiting queues into logically constrained term rewrite systems (LCTRSs, for short) has been proposed. To represent waiting queues, the transformation adopts a turn waiting system with number tickets, while the use of usual lists is a straightforward approach. In this abstract, we show a list-based approach to waiting queues and compare the two approaches by means of verification of race freedom of a simple reader-writer example.

A Nesting-Preserving Transformation of SIMP Programs into Logically Constrained Term Rewrite Systems Reviewed

Naoki Nishida, Misaki Kojima, and Ayuka Matsumi

Informal Proceedings of the 10th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2023) page： 1 - 11 2023.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

In the last decade, several transformations of an imperative program into a logically constrained term rewrite system (LCTRS, for short) have been investigated and extended. They do not preserve the nesting of statements, generating rewrite rules like transition systems, while function calls are represented by the nesting of function symbols. Structural features of the original program must be often useful in analyzing the transformed LCTRS, but, to use such features, we have to know how to transform the program into the LCTRS, e.g., we keep the correspondence between statements in the program and the introduced auxiliary function symbols in the LCTRS. In this paper, we propose a nesting-preserving transformation of a SIMP program (a C integer program) into an LCTRS. The transformation is almost based on previous work and introduces the nesting of function symbols that correspond to statements in the original program. To be more precise, we propose a construction of a tree homomorphism which is used as a post-process of the transformation in previous work, i.e., which is applied to the LCTRS obtained from the program. As a correctness of the nesting-preserving transformation, we show that the tree homomorphism is sound and complete for the reduction of the LCTRS.

On Polynomial Interpretations Toward Termination of Logically Constrained Term Rewrite Systems with Bit Vector Arithmetic

Ayuka Matsumi, Naoki Nishida, Misaki Kojima, and Donghoon Shin

IEICE Technical Rerport Vol. 122 ( 432 ) page： 85 - 90 2023.3

Authorship：Corresponding author Language：Japanese Publishing type：Research paper (conference, symposium, etc.)

Logically constrained term rewrite systems with the bit-vector theory (BV-LCTRSs, for short) are useful as models of programs written in C or other languages. During a process of Rewriting Induction for equivalence verification, we need to frequently prove termination of rewrite systems obtained by adding rewriting rules for induction hypotheses into a given rewrite system. As for term rewrite systems, the dependency pair (DP, for short) framework is used for proving termination of LCTRSs, and several kinds of DP processors are used in the framework. However, the polynomial interpretation processor, one of the most powerful processors in proving termination of LCTRSs with the integer theory, is not applicable to BV-LCTRSs. In this article, we aim at enhancing the power of proving termination of BV-LCTRSs. To this end, we propose the polynomial interpretation processor over bit-vectors and the single self-looping elimination processor as new DP processors for BV-LCTRSs.

From Starvation Freedom to All-Path Reachability Problems in Constrained Rewriting Reviewed International journal

Misaki Kojima and Naoki Nishida

Proceedings of the 25th International Symposium on Practical Aspects of Declarative Languages, Lecture Notes in Computer Science Vol. 13880 page： 161 - 179 2023.1

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings) Publisher：Springer, Cham

An all-path reachability problem of a logically constrained term rewrite system is a pair of constrained terms representing state sets, and is demonically valid if every finite execution path from any state in the first set to a terminating state includes a state in the second set. We have proposed a framework to reduce the non-occurrence of specified error states in a transition system represented by a logically constrained term rewrite system to an all-path reachability problem of the system. In this paper, we extend the framework to verification of starvation freedom of asynchronous integer transition systems with shared variables such that some processes enter critical sections.

DOI： 10.1007/978-3-031-24841-2_11

CO3 (Version 2.3)

Naoki Nishida and Misaki Kojima

Proceedings of the 11th International Workshop on Confluence page： 63 2022.8

Confluence Competition 2022 International coauthorship

Raul Gutierrez, Aart Middeldorp, Naoki Nishida, and Kiraku Shintani

Proceedings of the 11th International Workshop on Confluence page： 54 2022.8

On Transforming Imperative Programs into Logically Constrained Term Rewrite Systems via Injective Functions from Configurations to Terms Reviewed

Naoki Nishida, Misaki Kojima, and Takumi Kato

Informal Proceedings of the 9th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2022) page： 1 - 16 2022.7

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

To transform an imperative program into a logically constrained term rewrite system (LCTRS, for short), previous work converts a statement list to rewrite rules in a stepwise manner, and proves the correctness along such a conversion and the big-step semantics of the program. On the other hand, the small-step semantics of a programming language comprises of inference rules that define transition steps of configurations. Partial instances of such inference rules are almost the same as rewrite rules in the transformed LCTRS. In this paper, we aim at establishing a framework for plain definitions and correctness proofs of transformations from programs into LCTRSs. To this end, for the transformation in previous work, we show an injective function from configurations to terms, and reformulate the transformation by means of the injective function. The injective function maps a transition step to a reduction step, and results in a plain correctness proof.

On Reducing Non-Occurrence of Specified Runtime Errors to All-Path Reachability Problems of Constrained Rewriting Reviewed

Misaki Kojima and Naoki Nishida

Informal Proceedings of the 9th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2022) page： 1 - 16 2022.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

A concurrent program with semaphore-based exclusive control can be transformed into a logically constrained term rewrite system that is computationally equivalent to the program. In this paper, we first propose a framework to reduce the non-occurrence of a specified runtime error in the program to an all-path reachability problem of the transformed logically constrained term rewrite system. Here, an all-path reachability problem is a pair of state sets and is true if every finite execution path starting with a state in the first set and ending with a terminating state includes a state in the second set. Then, as a case study, we show how to apply the framework to the race-freeness of semaphore-based exclusive control in the program. Finally, we show a simplified variant of a proof system for all-path reachability problems.

On Transforming Rewriting-Induction Proofs for Logical-Connective-Free Sequents into Cyclic Proofs Reviewed

Shujun Zhang and Naoki Nishida

Informal Proceedings of the 9th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2022) page： 1 - 14 2022.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

A GSC-terminating and orthogonal inductive definition set (IDS, for short) of first-order predicate logic can be transformed into a many-sorted term rewrite system (TRS, for short) such that a quantifier-free sequent is valid w.r.t. the IDS if and only if a term equation representing the sequent is an inductive theorem of the TRS. Under certain assumptions, it has been shown that a quantifier- and cut-free cyclic proof of a sequent can be transformed into a rewriting-induction (RI, for short) proof of the corresponding term equation. The RI proof can be transformed back into the cyclic proof, but it is not known how to transform arbitrary RI proofs into cyclic proofs. In this paper, we show that for a quantifier- and logical-connective-free sequent, if there exists an RI proof of the corresponding term equation, then there exists a cyclic proof of some sequent w.r.t. some IDS such that the cyclic proof ensures the validity of the initial sequent. To this end, we show a transformation of the RI proof into such a cyclic proof, a sequent, and an IDS.

Transforming orthogonal inductive definition sets into confluent term rewrite systems Reviewed International journal

Shujun Zhang and Naoki Nishida

Journal of Logical and Algebraic Methods in Programming Vol. 127 page： 1 - 17 2022.6

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (scientific journal)

In this paper, we transform an orthogonal inductive definition set, which is a set of productions for inductive predicates, into a confluent term rewrite system such that a quantifier-free sequent is valid w.r.t. the inductive definition set if and only if an equation representing the sequent is an inductive theorem of the term rewrite system. To this end, we first propose a transformation of an orthogonal inductive definition set into a confluent term rewrite system that is equivalent to the inductive definition set in the sense of evaluating ground formulas. Then, we show that termination of the inductive definition set is proved by the generalized subterm criterion if and only if termination of the transformed term rewrite system is so. Finally, we show that the transformed term rewrite system with some rewrite rules for sequents has the expected property. In addition, we show a termination criterion for the union of term rewrite systems whose termination is proved by the generalized subterm criterion.

DOI： 10.1016/j.jlamp.2022.100779

On Transforming Cut- and Quantifier-Free Cyclic Proofs into Rewriting-Induction Proofs Reviewed International journal

Shujun Zhang and Naoki Nishida

Proceedings of the 16th International Symposium on Functional and Logic Programming (FLOPS 2022), Lecture Notes in Computer Science Vol. 13215 page： 262 - 281 2022.5

Authorship：Corresponding author Language：English Publishing type：Research paper (international conference proceedings) Publisher：Springer

An inductive definition set (IDS, for short) of first-order predicate logic can be transformed into a many-sorted term rewrite system (TRS, for short) such that a quantifier-free sequent is valid w.r.t. the IDS if and only if a term equation representing the sequent is an inductive theorem of the TRS. In this paper, to compare rewriting induction (RI, for short) with cyclic proof systems, under certain assumptions, we show that if a sequent has a cut- and quantifier-free cyclic proof, then there exists an RI proof for a term equation of the sequent. To this end, we propose a transformation of a cut- and quantifier-free cyclic proof of the sequent into an RI proof for the corresponding equation.

DOI： 10.1007/978-3-030-99461-7_15

Implementing Determinization of Term Rewrite Systems via Equivalence of Context-Free Expressions Toward Program Inversion

Himika Kumagai and Naoki Nishida

Record of the 84th National Convention of IPSJ page： 271 - 272 2022.3

On Constrained Rewrite Rules Representing Semantics Rules of LLVM IR

Takumi Kato, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 121 ( 318 ) page： 89 - 94 2022.1

Authorship：Corresponding author Language：Japanese Publishing type：Research paper (conference, symposium, etc.)

A method to verify programs written in a simple C-like language via logically constrained term rewrite systems (LCTRS, for short) has been investigated. The method transforms a program into an LCTRS, and reduces properties of the program to those of the transformed LCTRS. In this article, we propose a transformation of LLVM IRs into LCTRSs, aiming at expanding the scope of the method. In the semantics of LLVM IRs, a configuration includes a memory and an assignment as mappings in general. On the other hand, LCTRSs used in the existing work do not deal with such mappings as built-in data, and thus, function symbols keep ranges of memories and assignments as arguments, making the transformation and its correctness proof more complicated. For this reason, we employ LCTRSs that deal with memories and assignments as built-in data, as LLVM IRs do. This makes a correctness proof of our transformation clear. More precisely, we define an injective mapping from configurations to terms. Using the mapping, we propose a transformation that generates a rewrite rule for each instruction in an LLVM IR by instantiating each inference rule of the LLVM-IR semantics which is applicable to the instruction.

Lemma Generation by Lagrange Interpolation in Con- strained Rewriting Induction

Shinya Higa, Naoki Nishida, and Masahiko Sakai

Proceedings of the 38th Conference of Japan Society for Software Science and Technology page： 1 - 13 2021.9

Determinization of inverted grammar programs via context-free expressions Reviewed International journal

Naoki Nishida and Minami Niwa

Journal of Logical and Algebraic Methods in Programming Vol. 122 page： 1 - 26 2021.8

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal)

In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for testing and verifica- tion, among others. In this paper, we consider a subset of Erlang, a functional and concurrent programming language based on the actor model. We present a formal semantics for reversible computation in this language and prove its main properties, including its causal consistency. We also build on top of it a rollback operator that can be used to undo the actions of a process up to a given checkpoint.

DOI： 10.1016/j.jlamp.2021.100688

Other Link： http://hdl.handle.net/2237/0002001914

Confluence Competition 2021 International coauthorship

Aart Middeldorp, Naoki Nishida, Kiraku Shintani, and Johannes Waldmann

Proceedings of the 10th International Workshop on Confluence page： 51 2021.7

CO3 (Version 2.2)

Naoki Nishida

Proceedings of the 10th International Workshop on Confluence page： 61 2021.7

On Transforming Inductive Definition Sets into Term Rewrite Systems Reviewed

Shujun Zhang and Naoki Nishida

Informal Proceedings of the 8th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2021) page： 1 - 10 2021.7

Authorship：Last author,　Corresponding author Language：English Publishing type：Research paper (international conference proceedings)

In this paper, we transform an inductive definition set—a set of productions for inductive predicates—into a term rewrite system (TRS, for short) such that a quantifier-free sequent over the first-order logic with the inductive definition set is valid if and only if its corresponding equation is an inductive theorem of the TRS. The resulting TRS is composed of three parts: Rewrite rules for logical connectives and a binary symbol for sequents; rewrite rules for productions; rewrite rules for the co-patterns of the second part. For correctness of the resulting TRS, we assume a certain property of the inductive definition set, which is a sufficient condition for ground termination and ground confluence of the resulting TRS. The transformation aims at comparing cyclic proof systems and rewriting induction.

Transforming Programs with Counting Semaphores into Logically Constrained Term Rewrite Systems

Misaki Kojima, Naoki Nishida, and Masahiko Sakai

Record of the 83rd National Convention of IPSJ page： 229 - 230 2021.3

Speeding up combinatorial optimization solver CombSQL+ by introducing Pseudo-Boolean constraints

Junichiro Kishi, Masahiko Sakai, Naoki Nishida, and Kenji Hashimoto

IEICE Technical Rerport Vol. 120 ( 343 ) page： 66-71 2021.1

Language：Japanese

The authors have proposed a solver CombSQL+ for combinatorial optimization problems (COPs) described in extended SQL language. The system generates QFLIA constraints by executing an SQL query transformed from an input description, and then solves them by an SMT solver. This report proposes an improvement of the system to generate constraints in pseudo-Boolean forms if possible. We report that the enhancement accelerates more than seven times faster for a problem.

Reversible CSP Computations Reviewed

Carlos Galindo, Naoki Nishida, Josep Silva, and Salvador Tamarit

IEEE Transactions on Parallel and Distributed Systems Vol. 32 ( 6 ) page： 1425-1436 2021.1

Language：English Publishing type：Research paper (scientific journal)

Reversibility enables a program to be executed both forwards and backwards. This ability allows programmers to backtrack the execution to a previous state. This is essential if the computation is not deterministic because re-running the program forwards may not lead to that state of interest. Reversibility of sequential programs has been well studied and a strong theoretical basis exists. Contrarily, reversibility of concurrent programs is still very young, especially in the practical side. For instance, in the particular case of the Communicating Sequential Processes (CSP) language, reversibility is practically missing. In this article, we present a new technique, including its formal definition and its implementation, to reverse CSP computations. Most of the ideas presented can be directly applied to other concurrent specification languages such as Promela or CCS, but we center the discussion and the implementation on CSP. The technique proposes different forms of reversibility, including strict reversibility and causal-consistent reversibility. On the practical side, we provide an implementation of a system to reverse CSP computations that is able to highlight the source code that is being executed in each forwards/backwards computation step, and that has been optimized to be scalable to real systems.

DOI： 10.1109/TPDS.2021.3051747

ReverCSP: Time-Travelling in CSP Computations Reviewed

Carlos Galindo, Naoki Nishida, Josep Silva, and Salvador Tamarit

Proceedings of the 12th International Conference on Reversible Computation, Lecture Notes in Computer Science Vol. 12227 page： 239-245 2020.7

Language：English

This paper presents reverCSP, a tool to animate both forward and backward CSP computations. This ability to reverse computations can be done step by step or backtracking to a given desired state of interest. reverCSP allows us to reverse computations exactly in the same order in which they happened, or also in a causally-consistent way. Therefore, reverCSP is a tool that can be especially useful to comprehend, analyze, and debug computations. reverCSP is an open-source project publicly available for the community. We describe the tool and its functionality, and we provide implementation details so that it can be reimplemented for other languages.

DOI： 10.1007/978-3-030-52482-1_14

Confluence Competition 2020 International coauthorship

Aart Middeldorp, Naoki Nishida, Kiraku Shintani, and Johannes Waldmann

Proceedings of the 9th International Workshop on Confluence page： 53 2020.6

CO3 (Version 2.1)

Naoki Nishida

Proceedings of the 9th International Workshop on Confluence page： 67 2020.6

Transforming Concurrent Programs with Semaphores into Logically Constrained Term Rewrite Systems Reviewed

Misaki Kojima, Naoki Nishida, and Yutaka Matsubara

Informal Proceedings of the 7th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2020) page： 1-12 2020.6

A Case Study for Reversible Computing: Reversible Debugging of Concurrent Programs Reviewed

James Hoey, Ivan Lanese, Naoki Nishida, Irek Ulidowski, and German Vidal

Reversible Computation: Extending Horizons of Computing, Lecture Notes in Computer Science Vol. 12070 page： 108-127 2020.5

Language：English Publishing type：Research paper (scientific journal)

Reversible computing allows one to run programs not only in the usual forward direction, but also backward. A main application area for reversible computing is debugging, where one can use reversibility to go backward from a visible misbehaviour towards the bug causing it. While reversible debugging of sequential systems is well understood, reversible debugging of concurrent and distributed systems is less settled. We present here two approaches for debugging concurrent programs, one based on backtracking, which undoes actions in reverse order of execution, and one based on causal consistency, which allows one to undo any action provided that its consequences, if any, are undone beforehand. The first approach tackles an imperative language with shared memory, while the second one considers a core of the functional message-passing language Erlang. Both the approaches are based on solid formal foundations.

DOI： 10.1007/978-3-030-47361-7_5

Transforming Programs with Exclusive Control into Logically Constrained Term Rewrite Systems

Misaki Kojima, Naoki Nishida, Yutaka Matsubara, and Masahiko Sakai

IEICE Technical Rerport Vol. 119 ( 451 ) page： 31-36 2020.3

Language：Japanese

To apply Logically Constrained Term Rewrite Systems (LCTRSs, for short) to program verification, a previous work targets programs that are executed sequentially. Considering actual usage of computers, it has been expected to develop a verification method for equivalence between sequentially executed programs and their concurrent versions. In this paper, we propose a transformation of programs with exclusive control based on semaphores into LCTRSs, aiming at modeling concurrent programs by LCTRSs. To this end, we first expand arguments of a function symbol that has been introduced to represent a configuration of sequential execution, so as to store all executed processes. Next, we show how to represent operations for semaphores by rewrite rules, and show a transformation of programs with exclusive control based on semaphores into LCTRSs. We manage waiting lists for semaphores by means of number checks, avoiding recursive data structures such as lists.

Extending rewriting induction to existentially quantified equations

Kazushi Nishie, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 119 ( 246 ) page： 25-30 2019.10

Language：Japanese

In this paper, we extend rewriting induction which is developed to prove equations, to existentially quantified equations. More precisely, we first introduce existentially quantified terms into right-hand sides of rules in logically constrained term rewrite systems. Then, we formulate existentially quantified equations and extend rewriting induction for existentially quantified equations. Finally, we present an proof of inequalities by reducing them to existentially quantified equations and applying the extended rewriting induction.

CO3 (Version 2.0)

Naoki Nishida and Yuya Maeda

Proceedings of the Joint Proceedings of HOR 2019 and IWC 2019 (with system descriptions from CoCo 2019) page： 50 2019.6

Characterizing Compatible View Updates in Syntactic Bidirectionalization Reviewed

Naoki Nishida and German Vidal

Proceedings of the 11th International Conference on Reversible Computation, Lecture Notes in Computer Science Vol. 11497 page： 67-83 2019.6

Language：English

Given a function that takes a source data and returns a view, bidirectionalization aims at producing automatically a new function that takes a modified view and returns the corresponding, modified source. In this paper, we consider simple first-order functional programs specified by (conditional) term rewrite systems. Then, we present a bidirectionalization technique based on the injectivization and inversion transformations from. We also prove a number of relevant properties which ensure that changes in both the source and the view are correctly propagated and that no undesirable side-effects are introduced. Furthermore, we introduce the use of narrowing---an extension of rewriting that replaces matching with unification---to precisely characterize compatible (also called in-place) view updates so that the resulting bidirectional transformations are well defined. Finally, we discuss some directions for dealing with view updates that are not compatible.

DOI： 10.1007/978-3-030-21500-2_5

On Determinization of Inverted Grammar Programs via Context-Free Expressions Reviewed

Naoki Nishida and Minami Niwa

Informal Proceedings of the 6th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2018) page： 1-15 2019.6

Authorship：Lead author Language：English

In this paper, we propose a determinization method of inverted grammar programs by means of context-free expressions which are straightforward extensions of regular expressions to context-free languages. Grammar programs are context-free grammars that an inversion method proposed by Glueck and Kawabe uses as intermediate results. We use conditional term rewriting systems (CTRSs, for short) as target programs, and our determinization method aims at transforming a given CTRS into a non-overlapping one that is semantically equivalent to the given one. To this end, we first translate a grammar program into an equivalent context-free expression. Then, by using some simple equalities of expressions, we transform the expression to a desired form. Finally, we translate the resulting expression back into an equivalent grammar program which can be translated back into a non-overlapping CTRS.

On Formalizing a Transformation of IMP Programs into Logically Constrained Term Rewriting Systems in Isabelle/HOL Reviewed

Ryota Nakayama and Naoki Nishida

Informal Proceedings of the 6th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2018) page： 1-15 2019.6

Proving Program Equivalence with Constrained Rewriting Induction and Ctrl Reviewed

Caarsten Fuhs, Cynthia Kop, and Naoki Nishida

Informal Proceedings of the 3rd Workshop on Program Equivalence and Relational Reasoning page： 1-2 2019.4

Language：English Publishing type：Research paper (scientific journal)

We prove equivalence of imperative programs by an automatic conversion of the functions in the input program to an equivalent Logically Constrained Term Rewrite System (LCTRS), followed by constrained rewriting induction (either fully automatically or guided by the user) to analyze equivalence of the corresponding functions in the LCTRS. Our approach is implemented in the tool Ctrl.

SQL queries for generating input constraints of SMT solvers from descriptions of combinatorial optimization problems

Genki Sakanashi, Masahiko Sakai, Naoki Nishida, and Kenji Hashimoto

IEICE Technical Rerport Vol. 118 ( 471 ) page： 85-90 2019.3

Language：Japanese

The authors recently proposed an SQL-based language CombSQL+ for specifying combinatorial optimization problems, and showed a solving method that uses an SMT solver. This method has an advantage that problem constraints are written in ordinary SQL queries, and hence it enables us an intuitive specification. In order to generate constraints to be solved by an SMT solver from a specification, it uses SQL queries extended for constrained tables, each of which represents a set of tables. Current extended queries, however, does not cover full-SQL query facilities, hence for this we need to develop a complex SQL-engine for constrained tables. This paper proposes a generation method of an ordinary SQL query, whose execution by an existing SQL-engine causes constraints for SMT solvers. Here, a key technique is the use of user-definable functions that may cause side-effects allowed in the database system SQLite.

On Transforming Functions Accessing Global Variables into Logically Constrained Term Rewriting Systems Reviewed

Yoshiaki Kanazawa and Naoki Nishida

Electronic Proceedings in Theoretical Computer Science Vol. 289 page： 34-52 2019.2

Language：English

In this paper, we show a new approach to transformations of an imperative program with function calls and global variables into a logically constrained term rewriting system. The resulting system represents transitions of the whole execution environment with a call stack. More precisely, we prepare a function symbol for the whole environment, which stores values for global variables and a call stack as its arguments. For a function call, we prepare rewrite rules to push the frame to the stack and to pop it after the execution. Any running frame is located at the top of the stack, and statements accessing global variables are represented by rewrite rules for the environment symbol. We show a precise transformation based on the approach and prove its correctness.

DOI： 10.4204/EPTCS.289.3

arXiv

On Transforming Narrowing Trees into Regular Tree Grammars Generating Ranges of Substitutions Reviewed

Naoki Nishida and Yuya Maeda

Electronic Proceedings in Theoretical Computer Science Vol. 289 page： 68-87 2019.2

Language：English

The grammar representation of a narrowing tree for a syntactically deterministic conditional term rewriting system and a pair of terms is a regular tree grammar that generates expressions for substitutions obtained by all possible innermost-narrowing derivations that start with the pair and end with particular non-narrowable terms. In this paper, under a certain syntactic condition, we show a transformation of the grammar representation of a narrowing tree into another regular tree grammar that overapproximately generates the ranges of ground substitutions generated by the grammar representation. In our previous work, such a transformation is restricted to the ranges w.r.t. a given single variable, and thus, the usefulness is limited. We extend the previous transformation by representing the range of a ground substitution as a tuple of terms, which is obtained by the coding for finite trees. We show a precise definition of the transformation and prove that the language of the transformed regular tree grammar is an overapproximation of the ranges of ground substitutions generated by the grammar representation. We leave an experiment to evaluate the usefulness of the transformation as future work.

DOI： 10.4204/EPTCS.289.35

arXiv

On Representation of Structures and Unions in Logically Constrained Rewriting

Yoshiaki Kanazawa, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 118 ( 385 ) page： 67-72 2019.1

Language：Japanese

Recently, several methods for verifying imperative programs by means of transformations into term rewriting systems have been investigated. In particular, constrained rewriting systems are popular as sources of such transformations, since logical constraints used for modeling control flows can be separated from terms that represent intermediate states of the execution of target programs.In the existing methods, data types that can be used in target programs are, however, restricted to the integers and their one-dimensional arrays, and hence we are not allowed to use other primitive data types, structures, or unions.In this article, we propose a bit-vector representation of basic data types that are recursively defined over size-fixed primitive data types, structure, and unions in the framework of logically constrained rewriting, and then propose a construction of rewrite rules that access members of structures and unions.

Extending Narrowing Trees to Basic Narrowing in Term Rewriting

Yuya Maeda, Naoki Nishida, Masahiko Sakai, and Tomoya Kobayashi

IEICE Technical Rerport Vol. 118 ( 385 ) page： 73-78 2019.1

Loop Detection by Logically Constrained Term Rewriting Reviewed

Naoki Nishida and Sarah Winkler

Proceedings of the 10th Working Conference on Verified Software: Theories, Tools, and Experiments (VSTTE 2018), Lecture Notes in Computer Science Vol. 11294 page： 309-321 2018.11

Language：English

Logically constrained rewrite systems constitute a very general rewriting formalism that can capture simplification processes in various domains as well as computation in imperative programs. In both of these contexts, nontermination is a critical source of errors. We present new criteria to find loops in logically constrained rewrite systems which are implemented in the tool Ctrl. We illustrate the usefulness of these criteria in three example applications: to find loops in LLVM peephole optimizations, to detect looping program executions of C programs, and to establish nontermination of integer transition systems.

DOI： 10.1007/978-3-030-03592-1_18

A theory of reversibility for Erlang Reviewed

Ivan Lanese, Naoki Nishida, Adrian Palacios, and German Vidal

Journal of Logical and Algebraic Methods in Programming Vol. 100 page： 71-97 2018.11

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1016/j.jlamp.2018.06.004

On Simplification of C Programs for Asymptotic Complexity Analysis via Rewriting Analysis Tools

Kazushi Nishie, Naoki Nishida, and Masahiko Sakai

Record of 2018 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M1-5 ) page： 1 2018.9

On extention of narrowing trees to basic narrowing

Yuya Maeda, Naoki Nishida, and Masahiko Sakai

Record of 2018 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M1-56 ) page： 1 2018.9

Convergence of Simultaneously and Sequentially Unraveled TRSs for Normal Conditional TRSs Reviewed

Naoki Nishida, Yuta Tsuruta, and Yoshiaki Kanazawa

Proceedings of the 7th International Workshop on Confluence (IWC 2018) page： 51-55 2018.7

Authorship：Lead author Language：English

Unravelings, which are transformations of a conditional term rewriting system (CTRS, for short) into an unconditional term rewriting system (TRS, for short), are useful to prove confluence and operational termination of some CTRSs. A simultaneous unraveling has been proposed for normal 1-CTRSs and a sequential one has been proposed for deterministic 3-CTRSs, the class of which includes normal 1-CTRSs. In this paper, we first show that for a normal 1-CTRS, the simultaneously unraveled TRS is orthogonal iff so is the sequentially unraveled one. Then, we show that for a normal 1-CTRS, if the simultaneously unraveled TRS is terminating, then so is the sequentially unraveled one. Finally, we show that for a normal 1-CTRS with termination of the unraveled TRS, the simultaneously unraveled TRS is locally confluent iff so is the sequentially unraveled one.

CO3 (Version 1.5)

Naoki Nishida, Yuta Tsuruta, and Yoshiaki Kanazawa

Proceedings of the 7th International Workshop on Confluence (IWC 2018) page： 64 2018.7

Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems Reviewed

Naoki Nishida and Yuya Maeda

Proceedings of the 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), LIPIcs Vol. 108 page： 26:1-26:20 2018.6

Authorship：Lead author Language：English

A narrowing tree for a constructor term rewriting system and a pair of terms is a finite representation for the space of all possible innermost-narrowing derivations that start with the pair and end with non-narrowable terms. Narrowing trees have grammar representations that can be considered regular tree grammars. Innermost narrowing is a counterpart of constructor-based rewriting, and thus, narrowing trees can be used in analyzing constructor-based rewriting to normal forms. In this paper, using grammar representations, we extend narrowing trees to syntactically deterministic conditional term rewriting systems that are constructor systems. We show that narrowing trees are useful to prove two properties of a normal conditional term rewriting system: one is infeasibility of conditional critical pairs and the other is quasi-reducibility.

DOI： 10.4230/LIPIcs.FSCD.2018.26

Confluence Competition 2018

Takahito Aoto, Makoto Hamana, Nao Hirokawa, Aart Middeldorp, Julian Nagele, Naoki Nishida, Kiraku Shintani, and Harald Zankl

Proceedings of the 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), LIPIcs Vol. 108 page： 32:1-32:5 2018.6

CauDEr: A Causal-Consistent Reversible Debugger for Erlang Reviewed

Ivan Lanese, Naoki Nishida, Adrian Palacios, and German Vidal

Proceedings of the 14th International Conference on Functional and Logic Programming, Lecture Notes in Computer Scienc Vol. 10818 page： 247-263 2018.4

Language：English

Programming languages based on the actor model, such as Erlang, avoid some concurrency bugs by design. However, other concurrency bugs, such as message order violations and livelocks, can still show up in programs. These hard-to-find bugs can be more easily detected by using causal-consistent reversible debugging, a debugging technique that allows one to traverse a computation both forward and backward. Most notably, causal consistency implies that, when going backward, an action can only be undone provided that its consequences, if any, have been undone beforehand. To the best of our knowledge, we present the first causal-consistent reversible debugger for Erlang, which may help programmers to detect and fix various kinds of bugs, including message order violations and livelocks.

DOI： 10.1007/978-3-319-90686-7_16

Rewriting induction for constrained inequalities Reviewed

Takahiro Nagao and Naoki Nishida

Science of Computer Programming Vol. 155 page： 76-102 2018.4

Language：English Publishing type：Research paper (scientific journal)

Rewriting induction (RI) frameworks consist of inference rules to prove equations to be inductive theorems of a given term rewriting system, i.e., to be inductively valid w.r.t. reduction of the given system. To prove inductive validity of inequalities within such frameworks, one may reduce inequalities to equations. However, it is often hard to prove inductive validity of such reduced equations within the existing RI frameworks due to their indirect handling of inequalities. In this paper, we adapt the notion of inductive theorems to inequalities and propose an RI framework for directly proving inductive validity of inequalities of constrained term rewriting systems. Direct handling of inequalities enables us to utilize transitivity of binary predicates via application of induction hypotheses. Our framework succeeds in proving inductive validity of some inequalities that are hard to verify within the existing RI frameworks for equations. For the sake of automated reasoning, we provide a strategy for applying inference rules and evaluate its performance by means of an implementation.

DOI： 10.1016/j.scico.2017.10.012

Transforming Proof Tableaux of Hoare Logic into Inference Sequences of Rewriting Induction Reviewed

Shinnosuke Mizutani and Naoki Nishida

Electronic Proceedings in Theoretical Computer Science Vol. 265 page： 35-51 2018.2

Language：English

A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an inference sequence of rewriting induction for constrained rewriting. We also show that the resulting sequence is a valid proof for an inductive theorem corresponding to the Hoare triple if the constrained rewriting system obtained from the program is terminating. Such a valid proof with termination of the constrained rewriting system implies total correctness of the program w.r.t. the Hoare triple. The transformation enables us to apply techniques for proving termination of constrained rewriting to proving total correctness of programs together with proof tableaux for partial correctness.

DOI： 10.4204/EPTCS.265.4

Transforming Dependency Chains of Constrained TRSs into Bounded Monotone Sequences of Integers Reviewed

Tomohiro Sasano, Naoki Nishida, Masahiko Sakai, and Tomoya Ueyama

Electronic Proceedings in Theoretical Computer Science Vol. 265 page： 83-97 2018.2

Language：English

In the dependency pair framework for proving termination of rewriting systems, polynomial interpretations are used to transform dependency chains into bounded decreasing sequences of integers, and they play an important role for the success of proving termination, especially for constrained rewriting systems. In this paper, we show sufficient conditions of linear polynomial interpretations for transforming dependency chains into bounded monotone (i.e., decreasing or increasing) sequences of integers. Such polynomial interpretations transform rewrite sequences of the original system into decreasing or increasing sequences independently of the transformation of dependency chains. When we transform rewrite sequences into increasing sequences, polynomial interpretations have non-positive coefficients for reducible positions of marked function symbols. We propose four DP processors parameterized by transforming dependency chains and rewrite sequences into either decreasing or increasing sequences of integers, respectively. We show that such polynomial interpretations make us succeed in proving termination of the McCarthy 91 function over the integers.

DOI： 10.4204/EPTCS.265.7

Reversible computation in term rewriting Reviewed

Naoki Nishida, Adrian Palacios, and German Vidal

Journal of Logical and Algebraic Methods in Programming Vol. 94 page： 128-149 2018.1

Language：English Publishing type：Research paper (scientific journal)

Essentially, in a reversible programming language, for each forward computation from state S to state S', there exists a constructive method to go backwards from state S' to state S. Besides its theoretical interest, reversible computation is a fundamental concept which is relevant in many different areas like cellular automata, bidirectional program transformation, or quantum computing, to name a few.

In this work, we focus on term rewriting, a computation model that underlies most rule-based programming languages. In general, term rewriting is not reversible, even for injective functions; namely, given a rewrite step t1 -> t2, we do not always have a decidable method to get t1 from t2. Here, we introduce a conservative extension of term rewriting that becomes reversible. Furthermore, we also define two transformations, injectivization and inversion, to make a rewrite system reversible using standard term rewriting. We illustrate the usefulness of our transformations in the context of bidirectional program transformation.

DOI： 10.1016/j.jlamp.2017.10.003

CO3 (Version 1.4)

Naoki Nishida, Yoshiaki Kanazawa,, and Karl Gmeiner

Proceedings of the 5th International Workshop on Confluence (IWC 2016) page： 73 2017.9

A Reversible Semantics for Erlang Reviewed

Naoki Nishida, Adrian Palacios, and German Vidal

Revised Selected Papers of the 26th International Conference on Logic-Based Program Synthesis and Transformation, Lecture Notes in Computer Science (LOPSTR 2016) Vol. 10184 page： 259-274 2017.7

Authorship：Lead author Language：English

In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for debugging and for enforcing fault-tolerance, among others. In this paper, we consider a subset of Erlang, a concurrent language based on the actor model, and formally introduce a semantics for reversible computation. To the best of our knowledge, this is the first attempt to define a reversible semantics for Erlang.

DOI： 10.1007/978-3-319-63139-4_15

A compiler that translates to Malbolge from a C-language subset containing recursive calls

Genki Sakanashi, Shohei Kobe, Masahiko Sakai, Naoki Nishida, and Kenji Hashimoto

IEICE Technical Rerport Vol. 117 ( 136 ) page： 145-150 2017.7

Language：Japanese

Malbolge is an esoteric programming language, which is promising to protect intellectual property rights due to its difficulty of analysis. It is, however, very difficult to program because of its peculiar instructions. Tackling this problem, pseudo-instruction sequences was developed as an intermediate language for generating Malbolge programs. Nevertheless it is still difficult to program compared with ordinary languages like C. In this article, we present how to implement a compiler that translates to Malbolge from a C-language subset containing the integer type, the Boolean type, basic control structures such as while statement, and recursive calls. In the implementation, we firstly added array syntax and function syntax to pseudo-instruction sequences, and strengthen existing tools for the extention to conform with it. We next propose a translation method from C-language subset to pseudo-instruction sequences.

Polynomial Interpretations to Convert Dependency Chains of Constrained Term Rewriting Systems to Bounded Increasing Sequences of Integers

Tomohiro Sasano, Naoki Nishida, Masahiko Sakai, and Tomoya Ueyama

IEICE Technical Rerport Vol. 117 ( 136 ) page： 139-144 2017.7

Language：Japanese

In dependency pair framework for proving termination of constrained term rewriting systems, polynomial interpretations that transform dependency chains representing sequences of relevant function calls into bounded decreasing sequences of integers play an important role for the success of proving termination. In this article, we propose polynomial interpretations that transform dependency chains into bounded decreasing sequences but transform rewrite sequences of the original system into increasing sequences.We also propose polynomial interpretations that transform dependency chains into bounded increasing sequences of integers.
We report empirical comparison results between the proposed polynomial interpretations.

Verifying Procedural Programs via Constrained Rewriting Induction Reviewed

Carsten Fuhs, Cynthia Kop, and Naoki Nishida

ACM Transactions on Computational Logic Vol. 18 ( 2 ) page： 14:1-14:50 2017.6

Language：English Publishing type：Research paper (scientific journal)

This article aims to develop a verification method for procedural programs via a transformation into logically constrained term rewriting systems (LCTRSs). To this end, we extend transformation methods based on integer term rewriting systems to handle arbitrary data types, global variables, function calls, and arrays, and to encode safety checks. Then we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can automatically verify memory safety and prove correctness of realistic functions. Our approach proves equivalence between two implementations; thus, in contrast to other works, we do not require an explicit specification in a separate specification language.

DOI： 10.1145/3060143

Proving Confluence of Hierarchical Conditional Term Rewriting Systems without Sufficient Completeness

Takayuki Kuroda, Naoki Nishida, and Hiroyuki Seki

IEICE Technical Rerport Vol. 116 ( 512 ) page： 103-108 2017.3

Language：Japanese

A transformational approach to confluence proofs for conditional term rewriting systems (CTRS) has been investigated, but confluence of a CTRS defining sorting over natural numbers has not been proved yet by any existing confluence prover. Such a CTRS defines behavior of function symbols hierarchically, called a hierarchical CTRS, and is not sufficiently complete. In this article, we propose a method to prove confluence of hierarchical CTRSs that are not sufficiently complete. More precisely, we first extend rewriting induction for conditional equations to TRSs that are not sufficiently complete, and then we prove joinability of a conditional critical pair by inducing other conditions from the original conditional part. Next, we design a simplification order that takes conditional parts of rewrite rules into account, and propose a method to prove termination of hierarchical CTRSs by means of the designed simplification order.

Relative Termination via Dependency Pairs Reviewed

Jose Iborra, Naoki Nishida, German Vidal, and Akihisa Yamada

Journal of Automated Reasoning Vol. 58 ( 3 ) page： 391-411 2017.3

Language：English Publishing type：Research paper (scientific journal)

A term rewrite system is terminating when no infinite reduction sequences are possible. Relative termination generalizes termination by permitting infinite reductions as long as some distinguished rules are not applied infinitely many times. Relative termination is thus a fundamental notion that has been used in a number of different contexts, like analyzing the confluence of rewrite systems or the termination of narrowing. In this work, we introduce a novel technique to prove relative termination by reducing it to dependency pair problems. To the best of our knowledge, this is the first significant contribution to Problem #106 of the RTA List of Open Problems. We first present a general approach that is then instantiated to provide a concrete technique for proving relative termination. The practical significance of our method is illustrated by means of an experimental evaluation.

DOI： 10.1007/s10817-016-9373-5

Sound Structure-Preserving Transformation for Ultra-Weakly-Left-Linear Deterministic Conditional Term Rewriting Systems Reviewed

Ryota Nakayama, Naoki Nishida, and Masahiko Sakai

Proceedings of the 3rd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2016), Electronic Proceedings in Theoretical Computer Science Vol. 235 page： 62-77 2017.1

Language：English

In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is a sound structure-preserving transformation for weakly-left-linear deterministic conditional term rewriting systems. More precisely, we show that every weakly-left-linear deterministic conditional term rewriting system can be converted to an equivalent weakly-left-linear and ultra-weakly-left-linear deterministic conditional term rewriting system and prove that the SR transformation is sound for weakly-left-linear and ultra-weakly-left-linear deterministic conditional term rewriting systems. Here, soundness for a conditional term rewriting system means that reduction of the transformed unconditional term rewriting system creates no undesired reduction sequence for the conditional system.

DOI： 10.4204/EPTCS.235.5

arXiv

Notes on Confluence of Ultra-WLL SDCTRSs via a Structure-Preserving Transformation Reviewed

Naoki Nishida

Proceedings of the 5th International Workshop on Confluence (IWC 2016) page： 60-64 2016.9

Authorship：Lead author Language：English

A structure-preserving transformation proposed by Serbanuta and Rosu for strongly or syntactically deterministic conditional term rewriting systems (SDCTRSs) that are ultra-left-linear has been shown to be applicable to weakly-left-linear (WLL) and ultra-WLL SDCTRSs without any change, and sound for such DCTRSs even if they are not SDCTRSs. In this paper, we show a confluent, WLL, and ultra-WLL DCTRS that is not an SDCTRS such that the transformed TRS is not confluent. We also show that for a WLL and ultra-WLL SDCTRS, if the transformed TRS is confluent, then so is the SDCTRS.

CO3 (Version 1.3)

Naoki Nishida, Takayuki Kuroda, and Karl Gmeiner

Proceedings of the 5th International Workshop on Confluence (IWC 2016) page： 74 2016.9

Proving inductive validity of constrained inequalities Reviewed

Takahiro Nagao and Naoki Nishida

Proceedings of the 18th International Symposium on Principles and Practice of Declarative Programming (PPDP 2016) page： 50-61 2016.9

Language：English Publishing type：Research paper (scientific journal)

Rewriting induction (RI) frameworks consist of inference rules to prove equations to be inductive theorems of a given term rewriting system, i.e., to be inductively valid w.r.t. reduction of the given system. To prove inductive validity of inequalities within such frameworks, one may reduce inequalities to equations. However, it is often hard to prove inductive validity of such reduced equations within the existing RI frameworks due to their indirect handling of inequalities. In this paper, we adapt the notion of inductive theorems to inequalities and propose an RI framework for directly proving inductive validity of inequalities of constrained term rewriting systems. Within the framework, we handle inequalities that may contain function symbols defined in a given rewriting system but not necessarily interpreted by the built-in semantics. Direct handling of inequalities facilitates the utilization of transitivity of magnitude relations via inequalities obtained as induction hypotheses. Our approach succeeds in proving inductive validity of some inequalities that are hard to verify within the existing RI frameworks for equations.

DOI： 10.1145/2967973.2968598

An intermediate language for a compiler generating highly obfuscated Malbolge codes

Shohei Kobe, Masahiko Sakai, Naoki Nishida, and Hiroyuki Seki

IEICE Technical Rerport Vol. 116 ( 127 ) page： 105-110 2016.7

Reversible Term Rewriting Reviewed

Naoki Nishida, Adrian Palacios, and German Vidal

Proceedings of the 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016), LIPIcs Vol. 52 page： 28:1-28:18 2016.6

Language：English

Essentially, in a reversible programming language, for each forward computation step from state S to state S', there exists a constructive and deterministic method to go backwards from state S' to state S. Besides its theoretical interest, reversible computation is a fundamental concept which is relevant in many different areas like cellular automata, bidirectional program transformation, or quantum computing, to name a few. In this paper, we focus on term rewriting, a computation model that underlies most rule-based programming languages. In general, term rewriting is not reversible, even for injective functions; namely, given a rewrite step t1 -> t2, we do not always have a decidable and deterministic method to get t1 from t2. Here, we introduce a conservative extension of term rewriting that becomes reversible. Furthermore, we also define a transformation to make a rewrite system reversible using standard term rewriting.

DOI： 10.4230/LIPIcs.FSCD.2016.28

Reversible Term Rewriting in Practice Reviewed

Naoki Nishida, Adrian Palacios, and German Vidal

Informal Proceedings of the 3rd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2016) page： 77-85 2016.6

Language：English

A computation is considered reversible if, for each step from state S to state S', there exists a deterministic and terminating method to compute S back from S'. Reversibilization aims at producing a reversible version of an originally irreversible computation principle. Recently, we have introduced a reversible extension of term rewriting. Furthermore, we have defined an appropriate reversibilization transformation for rewrite systems so that standard rewriting becomes reversible on the transformed systems. In this paper, we focus on the potential applications of the reversibilization transformation. In particular, we show its application in the context of bidirectional program transformation and the reversibilization of cellular automata.

Extension of Separation Logic toward Verification of Functions Passed Arrays as Arguments

Shinnosuke Mizutani, Naoki Nishida, and Masahiko Sakai

the 109th Workshop on IPSJ Special Interest Group on Programming page： 1-8 2016.6

An extension of SQL for specifying combinatorial optimization problems

Yusaku Uchida, Masahiko Sakai, and Naoki Nishida

IEICE Technical Rerport Vol. 115 ( 508 ) page： 25-30 2016.3

Language：Japanese

The performance of satisfiability (SAT) solvers have incredibly improved in recent years. It is, however, difficult to design appropriate translators for solving combinatorial optimization problems by SAT-solvers. This paper proposes a description language for some combinatorial optimization problems by extending the syntax of the database query language SQL in order to enable their easy descriptions, and discusses a coding scheme of a problem specified by the language into a formula for SAT-solvers.

Program Verification Using Non-linear Loop Invariants Generated by Partially Applying an Extended Farkas' Lemma

Mawkish Yanagisawa, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 115 ( 508 ) page： 31-36 2016.3

Language：Japanese

To generate loop invariants, methods that, using Farkas' lemma, convert verification formulas obtained from a given template, a pre-condition, and a post-condtion of a program have been investigated. Farkas' lemma transforms formulas consisting of inequalities over linear polynomials into equivalent formulas. This lemma has been extended to deal with polynomials including non-linear monomials that may have function calls, and some examples that the extended Farkas' lemma succeeds in generating loop invariants having non-linear polynomials have been shown. However, it has not been discussed how useful the extended lemma is in verifying programs. In this paper, we evaluate the usefulness of a loop-invariant generation based on the extended Farkas' lemma, and propose a verification method that uses the extended lemma effectively. More precisely, using the extended lemma, we transform some of verification formulas that contain unknown coefficients for a given template, into another formula, and then we verify the validity of the formula obtained from the remaining formulas by applying an assignment for the unknown coefficients to satisfy the transformed formula.

Transforming Constrained Dependency Pairs by Narrowing

Tomohiro Sasano, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 115 ( 420 ) page： 123-128 2016.1

Language：Japanese

The dependency pair framework, a method for proving termination of term rewriting systems, has been extended for constrained term rewriting systems which are extensions of term rewriting systems by allowing rules to have guard constraints. In this paper, by removing one of the side conditions, we improve a narrowing-based transformation of constrained dependency pairs. More precisely, we show that the transformation is sound even if a dependency pair to be converted can form a self-chain such that there is no intermediate derivation.

On Proving Termination and Inductive Theorems Simultaneously for Constrained Term Rewriting Systems

Yoshifumi Kawamoto, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 115 ( 420 ) page： 75-80 2016.1

Constrained Term Rewriting tooL Reviewed

Cynthia Kop and Naoki Nishida

Proceedings of the 20th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Lecture Notes in Computer Science ( 9450 ) page： 549-557 2015.11

Language：English

This paper discusses Ctrl, a tool to analyse - both automatically and manually - term rewriting with logical constraints. Ctrl can be used with TRSs on arbitrary underlying logics, and automatically analyse various properties such as termination, confluence and quasi-reductivity. Ctrl also offers both a manual and automatic mode for equivalence tests using inductive theorem proving, giving support for and verification of "hand-written" term equivalence proofs.

DOI： 10.1007/978-3-662-48899-7_38

Maximum retaining number of learning clauses on SAT solvers for CNFs with cardinality clauses

Naohide Tsukamoto, Masahiko Sakai, Naoki Nishida, and Kenji Hashimoto

Record of 2015 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( A2-5 ) page： 1 2015.9

Reducing Relative Termination to Dependency Pair Problems Reviewed

Jose Iborra, Naoki Nishida, German Vidal, and Akihisa Yamada

Proceddings of the 25th International Conference on Automated Deduction (CADE 2015), Lecture Notes in Computer Science Vol. 9195 page： 163-178 2015.8

Authorship：Lead author Language：English

Relative termination, a generalized notion of termination, has been used in a number of different contexts like proving the confluence of rewrite systems or analyzing the termination of narrowing. In this paper, we introduce a new technique to prove relative termination by reducing it to dependency pair problems. To the best of our knowledge, this is the first significant contribution to Problem #106 of the RTA List of Open Problems. The practical significance of our method is illustrated by means of an experimental evaluation.

DOI： 10.1007/978-3-319-21401-6_11

CO3: a COnverter for proving COfluence of COnditional TRSs

Naoki Nishida, Takayuki Kuroda, Makishi Yanagisawa, and Karl Gmeiner

Proceedings of the 4th International Workshop on Confluence (IWC 2015) page： 42 2015.8

Confluence Competition 2015

Takahito Aoto, Nao Hirokawa, Julian Nagele, Naoki Nishida, and Harald Zankl

Proceddings of the 25th International Conference on Automated Deduction (CADE 2015), Lecture Notes in Computer Science Vol. 9195 page： 101-104 2015.8

An Equivalent Transformation of Constrained Term Rewriting Systems by Pattern Elimination

Takahiro Nagao, Naoki Nishida, and Masahiko Sakai

IEICE Technical Rerport Vol. 115 ( 153 ) page： 167-172 2015.7

Language：Japanese

A constrained term rewriting system, an extension of term rewriting systems, can control application of rules by constraints such as those on integers. By partial elimination of patterns occurring in left-hand sides of rules, which preserves their meanings, one can facilitate analyzing various properties. In this article, we propose a transformation based on pattern elimination of constrained term rewriting systems that contain only patterns of interpretable terms in their left-hand sides, and show sufficient conditions for the resulting system to be equivalent to the original with respect to some properties such as sufficient completeness and innermost termination. We also propose a procedure for testing reduction completeness as an application of the transformation.

Heuristics for Automatically Proving Commutativity of Function Composition for Constrained Term Rewriting Systems

Ryutaro Kuriki, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Rerport Vol. 114 ( 510 ) page： 91-96 2015.3

A Heuristic to Solve Inverse Unfolding Problem for Functions Dealing with Tree Structure Data

Tomofumi Kato, Masanori Nagashima, Masahiko Sakai, Naoki Nishida, and Toshiki Sakabe

IEICE Technical Rerport Vol. 114 ( 510 ) page： 85-90 2015.3

A framework for computing finite SLD trees Reviewed

Naoki Nishida and German Vidal

Journal of Logical and Algebraic Methods in Programming Vol. 84 ( 2 ) page： 197-217 2015.3

Language：English Publishing type：Research paper (scientific journal)

The search space of SLD resolution, usually represented by means of a so-called SLD tree, is often infinite. However, there are many applications that must deal with possibly infinite SLD trees, like partial evaluation or some static analyses. In this context, being able to construct a finite representation of an infinite SLD tree becomes useful.

In this work, we introduce a framework to construct a finite data structure representing the (possibly infinite) SLD derivations for a goal. This data structure, called closed SLD tree, is built using four basic operations: unfolding, flattening, splitting, and subsumption. We prove some basic properties for closed SLD trees, namely that both computed answers and calls are preserved. We present a couple of simple strategies for constructing closed SLD trees with different levels of abstraction, together with some examples of its application. Finally, we illustrate the viability of our approach by introducing a test case generator based on exploring closed SLD trees.

DOI： 10.1016/j.jlamp.2014.11.006

On Efficacy of Narrowing in Proving Termination of Constrained Term Rewriting Systems

Tomoya Ueyama, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Rerport Vol. 114 ( 416 ) page： 43-48 2015.1

Implementing a Conditional Dependency Pair Method for Proving Termination of Functional Programs with Exception Handling

Koichi Ota, Takeshi Hamaguchi, Masahiko Sakai, Akihisa Yamada, Naoki Nishida, and Toshiki Sakabe

IEICE Technical Rerport Vol. 114 ( 416 ) page： 55-60 2015.1

A Finite Representation of the Narrowing Space Reviewed

Naoki Nishida and German Vidal

Revised Selected Papers of the 23rd International Conference on Logic-Based Program Synthesis and Transformation, Lecture Notes in Computer Science Vol. 8901 page： 54-71 2014.12

Authorship：Lead author Language：English

Narrowing basically extends rewriting by allowing free vari- ables in terms and by replacing matching with unification. As a con- sequence, the search space of narrowing becomes usually infinite, as in logic programming. In this paper, we introduce the use of some operators that allow one to always produce a finite data structure that still rep- resents all the narrowing derivations. Furthermore, we extract from this data structure a novel, compact equational representation of the (pos- sibly infinite) answers computed by narrowing for a given initial term. Both the finite data structure and the equational representation of the computed answers might be useful in a number of areas, like program comprehension, static analysis, program transformation, etc.

DOI： 10.1007/978-3-319-14125-1

Automatic Constrained Rewriting Induction towards Verifying Procedural Programs Reviewed

Cynthia Kop and Naoki Nishida

Proceedings of the 12th Asian Symposium on Programming Languages and Systems (APLAS 2014) ( 8858 ) page： 334-353 2014.11

Authorship：Lead author Language：English

This paper aims at developing a verification method for procedural programs via a transformation into logically constrained term rewriting systems (LCTRSs). To this end, we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can handle realistic functions, involving, e.g., integers and arrays. An implementation is provided.

DOI： 10.1007/978-3-319-12736-1_18

A Simple Sufficient Condition for the Completeness of a Heuristic Procedure for Inverse Unfold Problem

Masanori Nagashima, Tomofumi Kato, Masahiko Sakai, and Naoki Nishida

IPSJ Special Interest Group on Programming ( 2014-3-(9) ) page： 1-7 2014.11

On Lemma Generation in Rewriting Induction for Constrained Term Rewriting Systems by Using Commutativity of Function Composition

Ryutaro Kuriki, Naoki Nishida, and Masahiko Sakai

Record of 2014 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M4-1 ) page： 1 2014.9

On a Necessary and Sufficient Condition for Equations to Represent Equivalence of Functions in Constrained Term Rewriting

Takumi Kataoka, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Record of 2014 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M4-4 ) page： 1 2014.9

On a Sufficient Condition for Argument Filterings to Preserve Equivalence between Functions in Term Rewriting

Yoshifumi Kawamoto, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Record of 2014 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M4-2 ) page： 1 2014.9

On a Procedure for Proving Confluence of Conditional Term Rewriting Systems by Using Condition Elimination

Makishi Yanagisawa, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Record of 2014 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M4-4 ) page： 1 2014.9

On Reducing the Frequency of Checking Validity of Presburger Formulas in the Dependency Pair Method for Constrained Term Rewriting Systems

Tomoya Ueyama, Naoki Nishida, Toshiki Sakabe, and Masahiko Sakai

Record of 2014 Tokai-Section Joint Conference on Electrical, Electronics, Information, and Related Engineering ( M4-5 ) page： 1 2014.9

On Improving Termination Preservability of Transformations from Procedural Programs into Rewrite Systems by Using Loop Invariants Reviewed

Naoki Nishida and Takumi Kataoka

Proceedings of the 14th International Workshop on Termination (WST 2014) page： 1-5 2014.7

Authorship：Lead author Language：English

Recently, to analyze procedural programs by using techniques in the field of term rewriting, several transformations of a program into a rewrite system have been developed. Such transformations are basically complete in the sense of computation, and e.g., termination of the rewrite system ensures termination of the program. However, in general, termination of the program is not preserved by the transformations and, thus, the preservation of termination is a common interesting problem. In this paper, we discuss the improvement of a transformation from a simple procedural program over integers into a constrained term rewriting system by appending loop invariants to loop conditions of "while" statements so as to preserve termination as much as possible.

Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems Reviewed

Karl Gmeiner and Naoki Nishida

Proceedings of the First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2014), OpenAccess Series in Informatics Vol. 40 page： 3-14 2014.7

Language：English

Transforming conditional term rewrite systems (CTRSs) into unconditional systems (TRSs) is a common approach to analyze properties of CTRSs via the simpler framework of unconditional rewriting. In the past many different transformations have been introduced for this purpose. One class of transformations, so-called unravelings, have been analyzed extensively in the past. In this paper we provide an overview on another class of transformations that we call structure-preserving transformations. In these transformations the structure of the conditional rule, in particular their left-hand side is preserved in contrast to unravelings. We provide an overview of transformations of this type and define a new transformation that improves previous approaches.

DOI： 10.4230/OASIcs.WPTE.2014.3

On Proving Confluence of Conditional Term Rewriting Systems via the Computationally Equivalent Transformation Reviewed

Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner

Proceedings of the 3rd International Workshop on Confluence (IWC 2014) page： 24-28 2014.7

Authorship：Lead author Language：English

This paper improves the existing criterion for proving confluence of a normal conditional term rewriting system (CTRS) via the Serbanuta-Rosu transformation, a computationally equivalent transformation of CTRSs into unconditional term rewriting systems (TRS), showing that a weakly left-linear normal CTRS is confluent if the transformed TRS is confluent. Then, we discuss usefulness of the optimization of the Serbanuta-Rosu transformation, which has informally been proposed in the literature.

Inverse Unfold Problem and Its Heuristic Solving Reviewed

Masanori Nagashima, Tomofumi Kato, Masahiko Sakai, and Naoki Nishida

Proceedings of the First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2014), OpenAccess Series in Informatics Vol. 40 page： 27-38 2014.7

Language：English

Unfold/fold transformations have been widely studied in various programming paradigms and are used in program transformations, theorem proving, and so on. This paper, by using an example, show that restoring an one-step unfolding is not easy, i.e., a challenging task, since some rules used by unfolding may be lost. We formalize this problem by regarding one-step program transformation as a relation. Next we discuss some issues on a specific framework, called pure-constructor systems, which constitute a subclass of conditional term rewriting systems. We show that the inverse of T preserves rewrite relations if T preserves rewrite relations and the signature. We propose a heuristic procedure to solve the problem, and show its successful examples. We improve the procedure, and show examples for which the improvement takes effect.

DOI： 10.4230/OASIcs.WPTE.2014.27

On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings Reviewed

Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner

Proceedings of the First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2014), OpenAccess Series in Informatics Vol. 40 page： 39-50 2014.7

Authorship：Lead author Language：English

In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs.

DOI： 10.4230/OASIcs.WPTE.2014.39

Inverse Unfold Problem and Its Heuristic Solving

Tomofumi Kato, Masanori Nagashima, Masahiko Sakai, and Naoki Nishida

IEICE Technical Rerport Vol. 113 ( 489 ) page： 13-18 2014.3

On Detecting Useless Transition Rules of Constrained Tree Automata

Yasuhiro Nakano, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Kenji Hashimoto

IEICE Technical Rerport Vol. 113 ( 489 ) page： 31-36 2014.3

Conversion to tail recursion in term rewriting Reviewed

Naoki Nishida and German Vidal

The Journal of Logic and Algebraic Programming Vol. 83 ( 1 ) page： 53-63 2014.1

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Tail recursive functions are a special kind of recursive functions where the last action in their body is the recursive call. Tail recursion is important for a number of reasons (e.g., they are usually more efficient). In this article, we introduce an automatic transformation of first-order functions into tail recursive form. Functions are defined using a (first-order) term rewrite system. We prove the correctness of the transformation for constructor-based reduction over constructor systems (i.e., typical first-order functional programs).

DOI： 10.1016/j.jlap.2013.07.001

On Constructing Constrained Tree Automata Recognizing Ground Instances of Constrained Terms Reviewed

Naoki Nishida, Masahiko Sakai, and Yasuhiro Nakano

Proceedings of the 2nd International Workshop on Trends in Tree Automata and Tree Transducers (TTATT 2013), Electronic Proceedings in Theoretical Computer Science Vol. 134 page： 1-10 2013.10

Authorship：Lead author Language：English

An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of constrained term rewriting systems enables us to relax the side conditions of some inference rules in the proving method. These two properties can be reduced to intersection emptiness problems related to sets of ground instances for constrained terms. This paper proposes a method to construct deterministic, complete, and constraint-complete constrained tree automata recognizing ground instances of constrained terms.

DOI： 10.4204/EPTCS.134.1

On Reducibility of Word Problems for Equations to Those for Ground Equations

Toshimitsu Sakai, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari and Naoki Nishida

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M4-4 ) page： 1 2013.9

Generation of Loop Invariants Consisting of Non-Linear Inequalities for Programs with Arrays

Junichiro Higashino, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari and Naoki Nishida

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M4-6 ) page： 1 2013.9

On Local Strategies for Automated Inductive-Theorem Proving on Simply Typed Term Rewriting Systems

Hisashi Kamiya, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe and Naoki Nishida

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M4-3 ) page： 1 2013.9

Designing Higher-order Lexicographic Path Ordering with Currying

Honami Matsubara, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe and Naoki Nishida

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M4-5 ) page： 1 2013.9

Development of an Interpreter Dynamically Checking Assertions on Pointers in Programs

Yoshihiro Mokutani, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari and Naoki Nishida

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M4-7 ) page： 1 2013.9

Use of Loop Invariants for Improving Termination Preservability of Transformations from Procedural Programs to Rewriting Systems

Takumi Kataoka, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe and Keiichirou Kusakari

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M2-6 ) page： 1 2013.9

Evaluation of Parallel Execution of an Implementation of Breadth-First-Search-based Completion Procedures in Erlang

Ryutaro Kuriki, Naoki Nishida, Toshiki Sakabe, Masahiko Sakai and Keiichirou Kusakari

Record of 2013 Tokai-Section Joint Conference on Electrical and Related Engineering ( M2-5 ) page： 1 2013.9

Term Rewriting with Logical Constraints Reviewed

Cynthia Kop and Naoki Nishida

Proceedings of the 9th International Symposium on Frontiers of Combining Systems, Lecture Notes in Artificial Intelligence ( 8152 ) page： 343-358 2013.9

Malbolge with 20trits word length and its programming support tool

Tatsuki Kato, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari and Naoki Nishida

IEICE Technical Rerport Vol. 113 ( 159 ) page： 73-78 2013.7

Proving Confluence of Conditional Term Rewriting Systems via Unravelings Reviewed

Karl Gmeiner, Naoki Nishida and Bernhard Gramlich

Proceedings of the 2nd International Workshop on Confluence page： 35-39 2013.6

Computing More Specific Versions of Conditional Rewriting Systems Reviewed

Naoki Nishida and German Vidal

Revised Selected Papers of the 22nd International Symposium on Logic-Based Program Synthesis and Transformation, Lecture Notes in Computer Science Vol. 7844 page： 137-154 2013.4

Improving Determinization of Grammar Programs for Program Inversion Reviewed

Minami Niwa, Naoki Nishida, and Masahiko Sakai

Revised Selected Papers of the 22nd International Symposium on Logic-Based Program Synthesis and Transformation, Lecture Notes in Computer Science Vol. 7844 page： 155-175 2013.4

On Composing the Simplex Method and Gomory Cut for Deriving Integer Assignments

Masaaki Fushimi, Naoki Nishida, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Rerport Vol. 112 ( 458 ) page： 109-114 2013.3

Construction of Constrained Tree Automata Recognizing Ground Instances of Constrained Terms

Yasuhiro Nakano, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Rerport Vol. 112 ( 373 ) page： 7-12 2013.1

Using SAT Solvers for Solving Control-Instruction Layout Problems in Low-Level Assembly Programming for Malbolge

Satoshi Ando, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari and Naoki Nishida

IEICE Technical Rerport Vol. 112 ( 373 ) page： 25-30 2013.1

A SAT Encoding for Finding Operation Sequences of Malbolge that Implement Trit-wise Functions

Satoshi Ando, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari and Naoki Nishida

IEICE Technical Rerport Vol. 112 ( 275 ) page： 7-12 2012.11

Formula transformation for sequential composition of Cooper's quantifier elimination and the general simplex method

Masaaki Fushimi, Naoki Nishida, Toshiki Sakabe, Masahiko Sakai, and Keiichirou Kusakari

Record of 2012 Tokai-Section Joint Conference on Electrical and Related Engineering ( A4-2 ) page： 1 2012.9

On Constructing Constrained Tree Automaton Recognizing Ground Instances of Constrained Terms

Yasuhiro Nakano, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

Record of 2012 Tokai-Section Joint Conference on Electrical and Related Engineering ( A4-4 ) page： 1 2012.9

Currying for Proving Termination of Simply-Typed Term Rewriting Systems

Keisuke Kurata, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

Record of 2012 Tokai-Section Joint Conference on Electrical and Related Engineering ( A4-3 ) page： 1 2012.9

Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity Invited Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Logical Methods in Computer Science Vol. 8 ( 3-4 ) page： 1-49 2012.8

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound w.r.t. reduction for every CTRS, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled TRS is left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling. Finally, we show that soundness of Ohlebusch's unraveling is the weakest in soundness of the other unravelings and a transformation, proposed by Serbanuta and Rosu, for (normal) deterministic CTRSs, i.e., soundness of them respectively implies that of Ohlebusch's unraveling.

DOI： 10.2168/LMCS-8(3:4)2012

On Extending Matching Operation in Grammar Programs for Program Inversion

Minami Niwa, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe and Keiichirou Kusakari

IEICE Technical Rerport Vol. 112 ( 164 ) page： 103-108 2012.7

Constrained Tree Automata and their Closure Properties Reviewed

Naoki Nishida, Futoshi Nomura, Katsuhisa Kurahashi and Masahiko Sakai

Proceedings of the 1st International Workshop on Trends in Tree Automata and Tree Transducers page： 24-34 2012.6

More Specific Term Rewriting Systems Reviewed

Naoki Nishida and German Vidal

Proceedings of the 21st International Workshop on Functional and (Constraint) Logic Programming page： 1-15 2012.5

Introducing Array Mechanism into High-Level Assembly Language for Malbolge

Satoshi Ando, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari and Naoki Nishida

IEICE Technical Rerport Vol. 112 ( 23 ) page： 43-49 2012.5

A Sound Type System for Typing Runtime Errors Reviewed

Akihisa Yamada, Keiichirou Kusakari, Toshiki Sakabe, Masahiko Sakai, and Naoki Nishida

IPSJ Transactions on Programming, Vol. 5 ( 2 ) page： 16-24 2012.3

On Rewriting Induction for Simply-typed Term Rewriting Systems

Akira Ozeki, Keiichirou Kusakari, Tsubasa Sakata, Naoki Nishida, Masahiko Sakai and Toshiki Sakabe

IEICE Technical Rerport Vol. 111 ( 406 ) page： 51-56 2012.1

On class of equation sets whose word problems are reducible to those of ground equation sets

Toshimitsu Sakai, Masahiko Sakai, Toshiki Sakabe, Naoki Nishida and Keiichirou Kusakari

IEICE Technical Rerport Vol. 111 ( 406 ) page： 45-49 2012.1

Automatic Generation of Non-linear Loop Invariants for Programs with Function Calls

Eiichi Suzuki, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari and Naoki Nishida

IEICE Technical Rerport Vol. 111 ( 406 ) page： 39-44 2012.1

On Usable Rules under Argument Filterings in Higher-Order Rewrite Systems

Kazuhiro Ooi, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe and Naoki Nishida

IEICE Technical Rerport Vol. 111 ( 406 ) page： 57-62 2012.1

Incorporating Elementary Symmetric Clauses into SAT Solvers with Two-Watched-Literal Scheme

Yoshizane Hino, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Rerport Vol. 111 ( 268 ) page： 67-72 2011.10

Verification of Equivalence between Functions in Constrained Term Rewriting Systems via Tree Homomorphisms

Kazuya Takakuwa, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

Proceedings of the 28th Conference of Japan Society for Software Science and Technology ( 7B-1 ) page： 1-12 2011.9

Disproving and Postulating for Multi-Context Rewriting Induction

Tsubasa Sakata, Naoki Nishida, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

Proceedings of the 28th Conference of Japan Society for Software Science and Technology ( 1A-4 ) page： 1-12 2011.9

Introducing Addition Instruction into High-Level Assembly Language for Malbolge

Satoshi Ando, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

Proceedings of the 28th Conference of Japan Society for Software Science and Technology ( 5A-3 ) page： 1-12 2011.9

On Automatic Generation of Loop Invariants for Programs with Function Calls

Eiichi Suzuki, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari and Naoki Nishida

Record of 2011 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( H1-5 ) page： 1 2011.9

Decidability of Termination for Linear Left-Shallow Term Rewriting Systems

Tatsuya Hattori, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

Record of 2011 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( H1-6 ) page： 1 2011.9

Decidability of Reachability for Right-shallow Context-sensitive Term Rewriting Systems Reviewed

Yoshiharu Kojima, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

IPSJ Transactions on Programming, Vol. 4 ( 4 ) page： 12-35 2011.9

Decidability and Undecidability of Reachability for Right-Linear Left-Shallow Non-Erasing Term Rewriting Systems

Yoshiharu Kojima, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

LA Symposium 2011 Summer ( 15 ) page： 1-10 2011.7

On Proving Termination of Constrained Term Rewrite Systems by Eliminating Edges from Dependency Graphs Reviewed

Tsubasa Sakata, Naoki Nishida, and Toshiki Sakabe

Proceedings of the 20th International Workshop on Functional and (Constraint) Logic Programming, Lecture Notes in Computer Science Vol. 6816 page： 138-155 2011.7

Language：English

In this paper, we propose methods for proving termination of constrained term rewriting systems, where constraints are interpreted by built-in semantics given by users, and rewrite rules are assumed to be sound for the interpretation. To this end, we extend the dependency pair framework for proving termination of unconstrained term rewriting systems to constrained term rewriting systems. Moreover, we extend the dependency pair framework so that dependency pair processors take a subgraph of the dependency graph as input and they output a finite set of graphs which can be obtained by eliminating nodes and/or edges from the input graph.

DOI： 10.1007/978-3-642-22531-4_9

Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the 22nd International Conference on Rewriting Techniques and Applications, LIPICcs Vol. 10 page： 267-282 2011.5

Authorship：Lead author Language：English

Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound for every CTRS w.r.t. reduction, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for deterministic CTRSs is sound w.r.t. reduction if the corresponding unraveled TRSs are left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling.

DOI： 10.4230/LIPIcs.RTA.2011.267

Program Inversion for Tail Recursive Functions Reviewed

Naoki Nishida and German Vidal

Proceedings of the 22nd International Conference on Rewriting Techniques and Applications, LIPIcs Vol. 10 page： 283-298 2011.5

Authorship：Lead author Language：English

Program inversion is a fundamental problem that has been addressed in many different programming settings and applications. In the context of term rewriting, several methods already exist for computing the inverse of an injective function. These methods, however, usually return non-terminating inverted functions when the considered function is tail recursive. In this paper, we propose a direct and intuitive approach to the inversion of tail recursive functions. Our new technique is able to produce good results even without the use of an additional post-processing of determinization or completion. Moreover, when combined with a traditional approach to program inversion, it constitutes a promising approach to define a general method for program inversion. Our experimental results confirm that the new technique compares well with previous approaches.

DOI： 10.4230/LIPIcs.RTA.2011.283

Tree Automata with Constraints and their Closure-Properties

Katsuhisa Kurahashi, Masahiko Sakai, Naoki Nishida, Futoshi Nomura, Toshiki Sakabe, Keiichirou Kusakari

IEICE Technical Rerport Vol. 110 ( 458 ) page： 61-66 2011.3

On non-termination proof of right-linear and right-shallow term rewriting systems based on forward narrowing

Tatsuya Hattori, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari and Toshiki Sakabe

IEICE Technical Report SS2010-44 Vol. 110 ( 336 ) page： 31-36 2010.12

Proposal of Abstract DPLL Algorithm Modulo Equational Theories

Tatsuya Baba, Toshiki Sakabe, Naoki Nishida, Keiichirou Kusakari, and Masahiko Sakai

IEICE Technical Report SS2010-36 Vol. 110 ( 227 ) page： 49-54 2010.10

On Turing Compeleteness of an Esoteric Language, Malbolge

Satoshi Nagasaka, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2010-37 Vol. 110 ( 227 ) page： 55-60 2010.10

SAT Solver for CNF Formulas with Elementary Symmetric Clauses based on Two Counter Scheme

Yoshizane Hino, Masahiko Sakai, Keiichirou Kusakari, Toshiki Sakabe, and Naoki Nishida

Record of 2010 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( D3-5 ) page： 1 2010.8

Proposal of Abstract DPLL Algorithm Modulo Equational Theories

Tatsuya Baba, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

Record of 2010 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( D3-4 ) page： 1 2010.8

Efficient Verification of Equivalence between Functions in Constrained Term Rewriting Systems

Kazuya Takakuwa, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

Record of 2010 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( D3-6 ) page： 1 2010.8

Termination of Narrowing via Termination of Rewriting Reviewed

Naoki Nishida and Germán Vidal

Applicable Algebra in Engineering, Communication and Computing Vol. 21 ( 3 ) page： 177-225 2010.5

Goal-directed and Relative Dependency Pairs for Proving the Termination of Narrowing Reviewed

José Iborra, Naoki Nishida, and Germán Vidal

Postproceedings of the 19th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2009), Lecture Notes in Computer Science Vol. 6037 page： 52-66 2010.4

Proving Injectivity of Functions via Program Inversion in Term Rewriting Reviewed

Naoki Nishida and Masahiko Sakai

Proceedings of the 10th International Symposium on Functional and Logic Programming (FLOPS 2010), Lecture Notes in Computer Science Vol. 6009 page： 288-303 2010.4

Solving Satisfiability of CNF Formulas with Clauses based on Elementary Symmetric Functions Reviewed

Yohei Umano, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

The IEICE Transactions on Information and Systems Vol. J93-D ( 1 ) page： 1-9 2010.1

Program Generation Based on Transformation of Conditional Equations

Masanori Nagashima, Masahiko Sakai, Toshiki Sakabe, Naoki Nishida, and Keiichirou Kusakari

IEICE Technical Report SS2009-41 Vol. 109 ( 343 ) page： 37-42 2009.12

Argument Filtering and Usable Rules in Higher-Order Rewrite Systems

Sho Suzuki, Keiichirou Kusakari, Toshiki Sakabe, Masahiko Sakai, and Naoki Nishida

IEICE Technical Report SS2009-39 Vol. 109 ( 343 ) page： 25-30 2009.12

On Decidability of Context-Sensitive Termination for Right-Linear Right-Shallow Term Rewriting Systems

Yoshimasa Mishuku, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2009-40 Vol. 109 ( 343 ) page： 31-36 2009.12

Improving the Termination Analysis of Narrowing in Left-Linear Constructor Systems Reviewed

José Iborra, Naoki Nishida, and Germán Vidal

Proceedings of the 19th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2009) page： 9 pages 2009.9

Language：English

In this extended abstract, we introduce an extension of a previous technique
for proving the termination of narrowing. Basically, given a rewrite system
and an argument filtering, the previous technique required the filtered
program to be free of extra-variables. In this work, we transform the original
rewrite system so that, in some cases (namely when the filtered rewrite system
is left-shallow), termination can still be proved despite the occurrence of
extra-variables in the filtered system.

Lemma Generation Method in Rewriting Induction for Constrained Term Rewriting Systems

Naoki Nakabayashi, Naoki Nishida, Keiichirou Kusakari, Toshiki Sakabe, and Masahiko Sakai

Proceedings of the 26th Conference of Japan Society for Software Science and Technology (JSSST) ( 7B-2 ) page： 1-14 2009.9

Context-Sensitive Innermost Reachability is Decidable for Linear Right-Shallow Term Rewriting Systems Reviewed

Yoshiharu Kojima, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

IPSJ Transactions on Programming, Vol. 2 ( 3 ) page： 20-32 2009.7

Completion after Program Inversion of Injective Functions Reviewed

Naoki Nishida and Masahiko Sakai

Electronic Notes in Theoretical Computer Science Vol. 237 page： 39-56 2009.4

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Given a constructor term rewriting system that defines injective functions, the inversion compiler proposed
by Nishida, Sakai and Sakabe generates a conditional term rewriting system that defines the inverse relations
of the injective functions, and then the compiler unravels the conditional system into an unconditional term
rewriting system. In general, the resulting unconditional system is not (innermost-)confluent even if the
conditional system is (innermost-)confluent. In this paper, we propose a modification of the Knuth-Bendix
completion procedure, which is used as a post-processor of the inversion compiler. Given a confluent and
operationally terminating conditional system, the procedure takes the resulting unconditional systems as
input. When the procedure halts successfully, it returns convergent systems that are computationally
equivalent to the conditional systems. To adapt the modified procedure to the conditional systems that are
not confluent but innermost-confluent, we propose a simplified variant of the modified procedure. We report
that the implementations of the procedures succeed in generating innermost-convergent inverse systems for
all the examples we tried.

Rewriting Induction for Constrained Term Rewriting Systems Reviewed

Tsubasa Sakata, Naoki Nishida, Toshiki Sakabe, Masahiko Sakai, and Keiichirou Kusakari

IPSJ Transactions on Programming, Vol. 2 ( 2 ) page： 80-96 2009.3

Language：Japanese Publishing type：Research paper (scientific journal)

The implicit induction, which is one of induction principles for proving inductive
theorems of equational theories, has been extended to deal with constrained
term rewriting systems. It has been applied to a method for proving equivalence
of imperative programs. In this paper, we extend another induction principle,
the rewriting induction, to cope with the case of constrained term rewriting
systems, and show its correctness. We also propose a method for proving inductive
theorems being based on the extended rewriting induction. Moreover,
we show a technique to disprove inductive theorems.

Solving Satisfiability of CNF Formulas with Elementary Symmetric Functions

Yohei Umano, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2008-44 Vol. 108 ( 362 ) page： 31-36 2008.12

Decidability of Termination Properties for Term Rewriting Systems Consisting of Shallow Dependency Pairs

Keita Uchiyama, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2008-45 Vol. 108 ( 362 ) page： 37-42 2008.12

Behavior Analysis of Scalable CAN Protocol on a Bit-Error Channel

Kenji Ukai, Toshiki Sakabe, Hiroaki Takada, Ryo Kurachi, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2008-37 Vol. 108 ( 242 ) page： 61-66 2008.10

制約付き項書換え系における書換え帰納法

坂田翼, 西田直樹, 坂部俊樹, 酒井, 正彦, 草刈圭一朗

第71回情報処理学会・プログラミング研究会配布資料 page： 1-12 2008.10

A Preliminary Study on Behavior Analysis of Scalable CAN Protocol

Kenji Ukai, Toshiki Sakabe, Hiroaki Takada, Ryo Kurachi, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

Record of 2008 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( O-262 ) page： 1 2008.9

Approach to Procedural-program Verification Based on Implicit Induction of Constrained Term Rewriting Reviewed

Yuki Furuichi, Naoki Nishida, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

IPSJ Transactions on Programming, Vol. 1 ( 2 ) page： 100-121 2008.9

Language：Japanese Publishing type：Research paper (scientific journal)

In the field of procedural programming, several verification methods based
on model checking or Hoare logic have been proposed. On the other hand,
in the field of term rewriting, implicit induction and rewriting induction have
been widely studied as methods for proving inductive theorems. In this paper,
we try to take advantages of methods for proving inductive theorems in verifying
procedural functions written in a "while" language with natural number
type. More precisely, we propose a transformation from procedural programs to
constrained term rewriting systems whose constraints are in Presburger arithmetic,
and show that the transformation reduces the equivalence of procedural
programs to that of functions in rewrite systems. By verifying the equivalence
between rewrite systems, we verify the equivalence between the corresponding
procedural functions. To establish this approach, we extend Critical Pair
Theorem and the basic completion procedure for constrained systems.

Completion as Post-Process in Program Inversion of Injective Functions Reviewed

Naoki Nishida and Masahiko Sakai

Proceedings of the 8th International Workshop on Reduction Strategies in Rewriting and Programming (WRS'08) page： 61-75 2008.7

A Reduction Order for Orienting Equations in Theorem Proving of Constrained TRSs

Naoki Nishida, Tsubasa Sakata, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Report SS2008-20 Vol. 108 ( 173 ) page： 43-48 2008.7

On Rewriting Induction for Presburger-Constrained Term Rewriting Systems

Tsubasa Sakata, Naoki Nishida, Toshiki Sakabe, Masahiko Sakai, and Keiichirou Kusakari

IEICE Technical Report SS2008-1 Vol. 108 ( 64 ) page： 1-6 2008.5

A Type System for Analyzing Secure Information Flow in Object-Oriented Programs with Exception Handling Reviewed

Sho Kurokawa, Hiroaki Kuwabara, Shinichirou Yamamoto, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

The IEICE Transactions on Information and Systems Vol. J91-D ( 3 ) page： 757-770 2008.3

Error Detection with Soft Typing for Dynamically Typed Languages

Akihisa Yamada, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

IEICE Technical Report SS2007-58 Vol. 107 ( 505 ) page： 7-12 2008.3

Approach to Procedural-Program Verification Based on Implicit Induction

Yuki Furuichi, Naoki Nishida, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

the 68th Workshop on IPSJ Special Interest Group on Programming. page： 1-22 2008.3

A Sufficient Condition for Termination of Transformations from Equations to Rewrite Rules

Kiyotaka Mizuno, Naoki Nishida, Toshiki Sakabe, Masahiko Sakai, and Keiichirou Kusakari

IEICE Technical Report SS2007-61 Vol. 107 ( 505 ) page： 25-30 2008.3

Extending program-generation system GeneSys for allowing negation in equational specifications

Satoru Kondo, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2007-45 Vol. 107 ( 392 ) page： 43-48 2007.12

A Tool for Designing Sudoku Problems by Interactive Fill-in Approach

Yohei Umano, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2007-50 Vol. 107 ( 392 ) page： 73-78 2007.12

Proving Non-termination of Logic Programs by Detecting Loops in Derivation Trees

Tomohiro Mizutani, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2007-30 Vol. 107 ( 275 ) page： 1-6 2007.10

Finding Magic Squares Based on CNF Encoding

Hiroyuki Ito, Masahiko Sakai, Keiichirou Kusakari, Toshiki Sakabe, and Naoki Nishida

Record of 2007 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( O-012 ) page： 1 2007.9

Recognizable Approximation of Descendant Sets for Left-Linear Oriented Conditional Term Rewriting Systems

Toshiki Murata, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2007-16 Vol. 107 ( 176 ) page： 1-6 2007.8

Implicit Induction for Proving Behavioral Equivalence by Equational Rewriting

Yuji Sasada, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2007-17 Vol. 107 ( 176 ) page： 7-12 2007.8

* Transformation for Refining Unraveled Conditional Term Rewriting Systems Reviewed

Naoki Nishida, Tomohiro Mizutani, and Masahiko Sakai

Electronic Notes in Theoretical Computer Science Vol. 174 ( 10 ) page： 75-95 2007.7

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Unravelings, transformations from conditional term rewriting systems (CTRSs, for short) into unconditional
term rewriting systems, are valuable for analyzing properties of CTRSs. In order to completely simulate
rewrite sequences of CTRSs, the restriction by a particular context-sensitive and membership condition that
is determined by extra function symbols introduced due to the unravelings, must be imposed on the rewrite
relations of the unraveled CTRSs. In this paper, in order to weaken the context-sensitive and membership
condition, we propose a transformation applied to the unraveled CTRSs, that reduces the number of the
extra symbols. In the transformation, updating the context-sensitive condition properly, we remove the
extra symbols that satisfy a certain condition. If the transformation succeeds in removing all of the extra
symbols, we obtain the TRSs that are computationally equivalent with the original CTRSs.

Static Dependeycy Pair Method for Proving Termination of Higher-Order Rewriting Systems

Keiichirou Kusakari, Yasuo Isogai, , Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

IEICE Technical Report SS2007-12 Vol. 107 ( 99 ) page： 17-22 2007.6

Convergent Term Rewriting Systems for Inverse Computation of Injective Functions Reviewed

Naoki Nishida, Masahiko Sakai, and Terutoshi Kato

Proceedings of the 9th International Workshop on Termination (WST'07) page： 77-81 2007.6

Argument Filtering Method on Second-Order Rewriting System

Yasuo Isogai, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

IEICE Technical Report SS2007-13 Vol. 107 ( 99 ) page： 23-28 2007.6

Decidability of Innermost Termination for Semi-Constructor Term Rewriting Systems

Keita Uchiyama, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

Theory of Computer Science and Its Applications, RIMS Kokyuroku (LA Symposium 2006 Winter) Vol. 1554 page： 166-170 2007.5

Confluence of Length Preserving String Rewriting Systems is Undecidable

Yi Wang, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

Theory of Computer Science and Its Applications, RIMS Kokyuroku (LA Symposium 2006 Winter) Vol. 1554 page： 171-177 2007.5

Usable Rules and Labeling Product-Typed Terms for Dependency Pair Method in Simply-Typed Term Rewriting Systems Reviewed

Takahiro Sakurai, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

The IEICE Transactions on Information and Systems Vol. J90-D ( 4 ) page： 978-989 2007.4

Automated Theorem Prover HOPSYS on Simply-Typed Rewriting Systems

Akinori Kamada, Keiichirou Kusakari, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report SS2006-57 Vol. 106 ( 426 ) page： 7-12 2006.12

Approach to Software Verification Based on Transformation from Procedural Programs to Rewrite Systems

Yuki Furuichi, Naoki Nishida, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Report SS2006-41 (KBSE2006-17) Vol. 106 ( 324 ) page： 7-12 2006.10

Example Programs Generated by GeneSys and Proposal of Introduction Rule

Satoru Kondo, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2006-46 (KBSE2006-22) Vol. 106 ( 324 ) page： 37-42 2006.10

Security Analysis of Information Flow for An Object-Oriented Language with Exception Handling

Sho Kurokawa, Hiroaki Kuwabara, Shinichirou Yamamoto, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2006-42 (KBSE2006-18) Vol. 106 ( 324 ) page： 13-18 2006.10

Compiling Term Rewriting Systems Having Higher-Order Functions

Yuji Sasada, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari, and Naoki Nishida

Record of 2006 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( O-437 ) page： 1 2006.9

Unraveling for Conditional Term Rewriting Systems with Membership Constraints

Toshiki Murata, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

Record of 2006 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( O-438 ) page： 1 2006.9

Transformation for Refining Unraveled Conditional Term Rewriting Systems Reviewed

Naoki Nishida, Tomohiro Mizutani, and Masahiko Sakai

Proceedings of the 6th International Workshop on Reduction Strategies in Rewriting and Programming (WRS'06) page： 34-48 2006.8

Dependency Graph Method for Proving Termination of Narrowing Reviewed

Naoki Nishida and Koichi Miura

Proceedings of the 8th International Workshop on Termination (WST'06) page： 12-16 2006.8

Transformation of Equational Rewriting Systems for Removing some Equations.

Koichi Miura, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2006-14 Vol. 106 ( 120 ) page： 7-12 2006.6

Usable Rules and Labeling Product-Typed Term for Dependency Pair Method in Simply-Typed Term Rewriting Systems

Takahiro Sakurai, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

IEICE Technical Report SS2006-15 Vol. 106 ( 120 ) page： 13-18 2006.6

Secrecy Verification of Spi Calculus Based on Term Regular Expressions

Yoshihiko Tashiro, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2005-82 Vol. 105 ( 596 ) page： 35-40 2006.2

Lexicographic Path Ordering for Proving Termination of Functional Programs

Yumi Hoshino, Keiichirou Kusakari, Masahiko Sakai, Toshiki Sakabe, and Naoki Nishida

IEICE Technical Report SS2005-85 Vol. 105 ( 597 ) page： 13-18 2006.2

Secrecy Verification by Transforming Cryptographic Protocol Descriptions to Coloured Petri Nets

Daisuke Okuya, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2005-58 Vol. 105 ( 490 ) page： 19-24 2005.12

Decidability of Termination for Left-Linear Shallow Term Rewriting Systems and Related

Yi Wang, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Report COMP2005-50 Vol. 105 ( 499 ) page： 9-13 2005.12

Type Judgement System for Communication Error in Distributed JoinJAVA Programs

Masaki Saeki, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2005-67 Vol. 105 ( 491 ) page： 25-30 2005.12

On Completeness of Outermost Strategy for Overlapping TRSs

Atsushi Iwata, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Report SS2005-46 Vol. 105 ( 331 ) page： 39-44 2005.10

Proving Sufficient Completeness of Functional Programs based on Recursive Structure Analysis and Strong Computability Reviewed

Takahiro Sakurai, Keiichirou Kusakari, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the Forum on Information Technology 2005, Information Technology Letters ( LA-001 ) page： 1-4 2005.9

Verifying Cryptographic Protocols by Using Coloured Petri Nets

Daisuke Okuya, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

Record of 2005 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( O-198 ) page： 1 2005.9

Type Judgement Systems for Assuring Distributed JoinJAVA Programs Run Normally

Masaki Saeki, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

Record of 2005 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers ( O-306 ) page： 1 2005.9

Generation of Inverse Computation Programs of Constructor Term Rewriting Systems Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

the IEICE Transactions on Information and Systems Vol. J88-D-I ( 8 ) page： 1171-1183 2005.8

Decidability of Termination for Semi-Constructor Term Rewriting Systems

Yi Wang, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Report SS2005-46 Vol. 105 ( 228 ) page： 13-18 2005.8

On Proving Termination of Simply-Typed Term Rewriting Systems Based on Strong Computability

Keiichirou Kusakari, Takahiro Sakurai, Keiichirou Kusakari, Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report SS2005-21 Vol. 105 ( 129 ) page： 19-24 2005.6

Programming Method in Obfuscated Language Malbolge

Hisashi Iizawa, Toshiki Sakabe, Masahiko Sakai, Keiichirou Kusakari, and Naoki Nishida

IEICE Technical Report SS2005-22 Vol. 105 ( 129 ) page： 25-30 2005.6

Dependency Graph Method for Proving Termination of Narrowing

Koichi Miura, Naoki Nishida, Masahiko Sakai, Keiichirou Kusakari, and Toshiki Sakabe

IEICE Technical Report SS2005-23 Vol. 105 ( 129 ) page： 31-36 2005.6

Partial Inversion of Constructor Term Rewriting Systems Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the 16th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science Vol. 3467 page： 264-278 2005.4

変換と部分評価に基づく非左辺正規なメタ項の停止性証明

蛸島洋明, 酒井正彦, 坂部俊樹, 西田直樹, 草刈圭一朗

計算機科学基礎理論とその応用, 数理解析研究所講究録（2004年度冬のLAシンポジウム） Vol. 1426 page： 113-118 2005.4

弱最内戦略を完全にする項書換え系の等価変換

岡本晃治, 酒井正彦, 西田直樹, 草刈圭一朗, 坂部俊樹

計算機科学基礎理論とその応用, 数理解析研究所講究録（2004年度冬のLAシンポジウム） Vol. 1426 page： 119-125 2005.4

到達可能性の判定における成長TRSに対する手法と正規化規則による手法の関係

村田龍彦, 酒井正彦, 西田直樹, 草刈圭一朗, 坂部俊樹

計算機科学基礎理論とその応用, 数理解析研究所講究録（2004年度冬のLAシンポジウム） Vol. 1426 page： 106-112 2005.4

On Recursion Removal from Non-Linear Top-Recursive Programs

Yohei Takasu, Masahiko Sakai, Naoki Nishida, Keiichirou Kusakari, and Toshiki Sakabe

New Aspects of Theoretical Computer Science, RIMS Kokyuroku (LA Symposium 2004 Winter) Vol. 1426 page： 39-44 2005.4

Simulating Fusion Transformation by Program-Generation Transformation

Masanori Nagashima, Masahiko Sakai, Naoki Nishida, Toshiki Sakabe, and Keiichirou Kusakari

IEICE Technical Report SS2004-33 Vol. 104 ( 466 ) page： 43-48 2004.11

On Simulation-Completeness of Unraveling for Conditional Term Rewriting Systems

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report SS 2004-18 Vol. 104 ( 243 ) page： 25-30 2004.8

On Simulation-Completeness of Unraveling for Conditional Term Rewriting Systems

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

LA Symposium 2004 Summer ( 7 ) page： 1-6 2004.7

Improving Efficiency of of Computation of Right-Linear Constructor Term Rewriting Systems with Extra Variables Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Computer Software Vol. 21 ( 3 ) page： 40-47 2004.5

Narrowing-Based Simulation of Term Rewriting Systems with Extra Variables and its Termination Proof Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Electronic Notes in Theoretical Computer Science Vol. 86 ( 3 ) page： 1-18 2003.11

Computation Model of Term Rewriting Systems with Extra Variables Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Computer Software Vol. 20 ( 5 ) page： 85-89 2003.9

Improving Efficiency of of Computation of Right-Linear Constructor Term Rewriting Systems with Extra Variables

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the 20th Conference of Japan Society for Software Science and Technology (JSSST) ( 5B-3 ) page： 1-5 2003.9

Normal-form Computation by Left-most Innermost Narrowing on Right-Linear Overlay Term Rewriting Systems with Extra Variables

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

LA Symposium 2003 Summer ( 24 ) page： 1-6 2003.7

Narrowing-Based Simulation of Term Rewriting Systems with Extra Variables and its Termination Proof Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the 12th International Workshop on Functional and (Constraint) Logic Programming (WFLP'03) page： 198-211 2003.6

Narrowing-based Effective Rewriting and its Termination for Term Rewriting Systems with Extra Variables

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

New Aspects of Theoretical Computer Science, RIMS Kokyuroku (LA Symposium 2002 Winter) Vol. 1325 page： 238-243 2003.5

Narrowing-based Effective Rewriting and its Termination for Term Rewriting Systems with Extra Variables

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report COMP2003-68 Vol. 102 ( 593 ) page： 45-52 2003.1

A Narrowing-based Reduction of Term Rewriting Systems with Extra Variables

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Record of 2002 Tokai-section Joint Conference of the Eight Institutes of Electrical and Related Engineers page： 292 2002.9

A Computation Model of Term Rewriting Systems with Extra Variables

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the 19th Conference of Japan Society for Software Science and Technology (JSSST) ( 6F-3 ) page： 1-5 2002.9

Generation of a TRS Implementing the Inverses of Pure Treeless Functions Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Computer Software Vol. 19 ( 1 ) page： 29-33 2002.1

Generation of a TRS Implementing the Inverses of the Functions with Specified Arguments Fixed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report COMP2001-67 Vol. 101 ( 488 ) page： 33-40 2001.12

Generation of Inverse Term Rewriting Systems for Pure Treeless Functions Reviewed

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the International Workshop on Rewriting in Proof and Computation (RPC'01) page： 188-198 2001.10

Generation of a TRS Implementing the Inverses of Pure Treeless Functions

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

Proceedings of the 18th Conference of Japan Society for Software Science and Technology (JSSST) ( 6C-3 ) page： 1-5 2001.9

Generation of a Conditional TRS Implements the Inverses of Pure Treeless Functions

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report COMP2001-14 Vol. 101 ( 133 ) page： 9-16 2001.6

Designing Unlimited Size Resource C-Libraries Freeing Users from GC Annoyance

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

IEICE Technical Report SS2000-9 Vol. 100 ( 64 ) page： 25-32 2000.5

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