受賞区分：国内学会・会議・シンポジウム等の賞  受賞国：日本国

受賞区分：国内学会・会議・シンポジウム等の賞  受賞国：日本国

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

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

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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.

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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.

担当区分：責任著者   記述言語：日本語   掲載種別：研究論文（研究会，シンポジウム資料等）  

ビットベクトル制約付き項書換え系（BV-LCTRS）はC言語などのプログラムのモデルとして有用である．等価性検証に書換え帰納法を用いる際には，与えられた書換え系に帰納法の仮定となる書換え規則を加えて得られる書換え系の停止性が何度も証明される. LCTRSの停止性証明には項書換え系と同様に依存対プロセッサを使用して証明する枠組みの依存対フレームワークが用いられるが，整数制約を持つLCTRSの停止性証明において最も強力なプロセッサの1つである多項式解釈プロセッサはBV-LCTRSには適用できない．本稿では，BV-LCTRSの停止性証明を強化することを目的として，新たな依存対プロセッサとしてビットベクトル上の多項式解釈プロセッサと単一自己ループ除去プロセッサを提案する．

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：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

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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.

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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.

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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.

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

担当区分：責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：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

担当区分：責任著者   記述言語：日本語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：責任著者   記述言語：日本語   掲載種別：研究論文（研究会，シンポジウム資料等）  

C言語に沿った簡易プログラミング言語を論理制約付き項書換え系（LCTRS）に変換し，元のプログラムの性質をLCTRSの性質に帰着して検証する手法が研究されている．本稿では，LCTRSへ変換できるプログラミング言語を増やすことをめざし，LLVM中間表現からLCTRSへの変換を提案する．一般に，LLVM中間表現の意味論ではメモリ及び変数への割当てが写像として計算状態に含まれる．一方，写像をデータとして扱わないLCTRSへの既存の変換では写像の値域を関数記号の引数として保持させることになり正当性証明を複雑にする．本稿ではメモリ及び割当てに相当する写像をデータとして扱うLCTRSを用いることで，変換とその正当性証明を簡潔にする．具体的には，プログラムの計算状態から項への単射関数を定義し，LLVM中間表現の各命令とそれに適用可能な各意味論規則に対して，1つの制約付き書換え規則を生成する．

担当区分：責任著者   記述言語：日本語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

その他リンク： http://hdl.handle.net/2237/0002001914

記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：最終著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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.

担当区分：責任著者   記述言語：日本語   掲載種別：研究論文（研究会，シンポジウム資料等）  

記述言語：日本語  

著者らはこれまでに，拡張したSQLで組合せ最適化問題を簡単に記述でき，かつ効率的に解くことのできる求解系CombSQL+を提案した．CombSQL+はシステム内部で，入力のSQL式からプログラム変換によって得られるSQL式をDBエンジンで実行することでいくつかの線形整数制約（QFLIA）を生成し，SMTソルバを利用してそれらの解を求めている．本稿では，変換後のSQL式で用いられる制約生成関数を工夫することで，擬ブール制約として表現できる制約を直接，擬ブール制約として生成する方法を提案する．この改良により問題によっては7倍以上の高速化が達成できたことを報告する．

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：英語  

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

記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（研究会，シンポジウム資料等）  

記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：日本語  

計算モデルである論理制約付き項書換え系（LCTRS）をプログラムの検証に用いる先行研究では，逐次実行される命令型プログラムを対象としている．現実の計算機の利用状況を考えると，逐次実行されるプログラムとそれを並行化したプログラムが等価であることを検証したいという要求がある．本稿では，並行実行されるプログラムをLCTRSで表現すること目的として，セマフォによる排他制御を含むプログラムをLCTRSで表現する方法を提案する．そのためにまず，先行研究で導入された実行環境を表す関数記号の引数を，実行されるプロセスの数だけ増やすことで，プロセスの並行実行を表現する．次に，セマフォに対する操作を書換え規則で表現し，セマフォによる排他制御を含むプログラムをLCTRSに変換する．セマフォに対する待ち行列を番号札を使って管理することで，リストなどの再帰データ構造を導入せずにセマフォの操作を表現する．

記述言語：日本語  

本稿では，等式を証明するための書換え帰納法を存在限量子付き等式を証明できるように拡張する．具体的にはまず，論理制約付き項書換え系の書換え規則の右辺に存在限量子を持つ項を許すように拡張する．次に，存在限量子付き等式を形式化し，書換え帰納法を拡張する．最後に，不等式を存在限量子付き等式に帰着して証明する例を示す．

担当区分：筆頭著者   記述言語：英語  

記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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.

記述言語：英語  

In this paper, we aim at formalizing a transformation of an IMP program into a logically constrained term rewriting system (LCTRS, for short) in Isabelle/HOL. To this end, we formalize LCTRSs and the transformation in Isabelle/HOL.

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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.

記述言語：日本語  

著者らはこれまでに，組合せ最適化問題を簡単に記述でき，かつ効率的に解く手法を開発すること目的として，SQLを基礎とした言語CombSQL+を提案し，SMTソルバを利用した問題解法を示した．この手法の特長は，通常のSQL問い合わせをそのまま制約の記述に用いることができ，直観的な記述ができることにある．CombSQL+で書かれた問題記述からのSMTソルバに入力するための制約を生成するために，テーブルの集合を表す制約付きテーブル上に拡張したSQL問合せを利用している．しかしながらSQLのすべての問い合わせ機能には対応しておらず，対応のためには制約付きテーブル上に拡張した複雑なSQLエンジンを拡充する必要がある．本稿では，拡張SQLエンジンを拡充するのではなく，既存のSQLエンジンで実行するだけでSMTソルバに与える制約式を生成できるSQL問い合わせを生成する方法を提案する．ここで，データベースシステムSQLiteが備える，副作用をもつ関数が定義できるという機能を利用することが，SMTソルバに与える制約式の生成における鍵となっている．

記述言語：英語  

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

記述言語：英語  

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

記述言語：日本語  

近年，項書換え系への変換に基づいた手続き型のプログラムの検証について研究が行われており，実行の中間状態を表現する項から制御フローをモデル化するための論理制約を分離して表現できる論理制約付き項書換え系への変換が注目されている．しかし，既存手法ではデータ型として整数とその1次元配列のみをデータとして扱うC言語プログラムを対象としており，ビット数が異なる基本データ型や構造体，共用体を扱っていない．本稿では，構造体や共用体などのサイズの異なるデータ構造を論理制約付き項書換えの枠組みで扱うための，構造体や共用体のビットベクトルを用いた表現，およびそれらのメンバへアクセスするための書換え規則の構成法を提案する．

記述言語：日本語  

記述言語：英語  

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

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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.2018.06.004

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

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.

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

We report on the 2018 edition of the Confluence Competition, a competition of software tools that aim to (dis)prove confluence and related properties of rewrite systems automatically.

DOI： 10.4230/LIPIcs.FSCD.2018.32

記述言語：英語  

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

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：英語  

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

記述言語：英語  

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

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

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

記述言語：日本語  

難読プログラミング言語Malbolgeは，その解析困難性により知的財産権の保護などに役立つと考えられているが，命令が特殊であるためプログラムの作成は非常に困難である．そのため，Malbolgeプログラムを生成するための中間言語として制御付き疑似命令列が提案されているが，Cなどの通常の言語と比較すると依然としてプログラミングが困難である．本稿では，整数型と真偽型を扱え，while文などの基本的な制御構造と再帰関数を定義できるC言語のサブセットのプログラムからMalbolgeコードへのコンパイラの実現法を述べる．コンパイラの実現のために，まず，既存の制御付き疑似命令列に配列構文と関数構文を追加し，それにあわせて既存の制御付き疑似命令列からMalbolgeへの変換系を拡張する．さらにC言語のサブセットから制御付き疑似命令列へ変換する方法を提案する．

記述言語：日本語  

制約付き項書換え系の停止性証明の枠組みである依存対フレームワークでは，関数呼び出しの関係を表現した依存鎖を下限付き整数減少列に変換する多項式解釈が証明の成否を左右する重要な役割を果たす．本稿では，依存鎖を下限付き整数減少列に変換する一方で，書換え規則による書換え系列を整数増加列に変換する多項式解釈による停止性証明機能を依存対フレームワークに導入する．さらに，依存鎖を上限付き整数増加列に変換する多項式解釈による停止性証明機能を導入し，比較実験の結果を報告する．

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：日本語  

条件付き項書換え系（CTRS）における合流性の検証手法として項書換え系への変換を経て証明する手法が知られているが，自然数リストの並び替えを行うCTRSの合流性は証明できていない．このCTRSは関数記号の振舞いが階層的に定義される階層的CTRSとなっており，十分完全性を持っていない．本稿では，十分完全性を持たない階層的CTRSの合流性を証明する手法を提案する．具体的には，条件付き等式に対する書換え帰納法を十分完全性を持たないTRSに拡張し，書換え帰納法を用いて条件付き危険対の条件から別の条件を導出することでその危険対が会同可能であることを示す．次に，書換え規則の条件部が成立することを考慮できる単純化順序を設計し，その単純化順序により階層的CTRSの停止性を証明する手法を提案する．

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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.

担当区分：筆頭著者   記述言語：英語  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：日本語  

記述言語：英語  

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

記述言語：英語  

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.

記述言語：日本語  

記述言語：日本語  

近年，充足可能性判定ソルバの高速化がめざましい．しかしながらこれらのソルバを用いて組合せ最適化問題を解くための論理式へのコーディングは容易ではない．本稿では，組合せ最適化問題の定義の容易な記述を可能にするため，データベース問い合わせ言語SQLに対して組合せ最適化問題を記述するための構文を追加し，その記述から充足可能性判定ソルバを利用して問題の解を得るための手法について論ずる．

記述言語：日本語  

ループ不変式を生成するための手法として，与えたテンプレートと事前条件と事後条件から得られる検証式をFarkas補題に基づき変換する手法が研究されている．Farkas補題に基づく変換では線形な多項式の不等式のみを原始論理式として含む論理式を等価変換する．それを変数や関数適用項の積を単項式とする多項式上に拡張した拡張Farkas補題が提案され，非線形なループ不変式を生成できる場合があることが示された．しかし，拡張Farkas補題を用いて生成したループ不変式がプログラム検証に有効かどうかについては議論されていない．本稿では，プロラム検証における拡張Farkas補題に基づくループ不変式の生成法の有効性を評価し，拡張Farkas補題を有効に利用する検証手法を提案する．具体的には，未知係数を含む複数の検証式の一部を拡張Farkas補題により変換し，それを充足する未知係数の割り当てを残りの検証式の未知係数に代入した後に恒真性を判定する．

記述言語：日本語  

項書換え系の停止性証明の枠組みである依存対フレームワークは項書換え規則に制約を付随させた制約付き項書換え系を対象に拡張された．本論文では、拡張された依存対フレームワークにおけるナローイングによる依存対の変換の適用条件を緩和する．具体的には，先行研究における変換対象の依存対が直接接続可能でないという条件を満たさない場合にも変換が健全であることことを示す．

記述言語：日本語  

記述言語：英語  

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

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

記述言語：英語  

Confluence is one of the central properties of rewriting. Our competition aims to foster the development of techniques for proving/disproving confluence of various formalisms of rewriting automatically. We explain the background and setup of the 4th Confluence Competition.

DOI： 10.1007/978-3-319-21401-6_5

記述言語：日本語  

制約付き項書換え系は整数制約などにより規則の適用を制御できるように項書換え系を拡張した枠組みである．書換え規則の左辺に現れるパターンの一部を意味を変えることなく除去することにより，様々な性質の解析が容易となる．本稿では，左辺に解釈項のパターンのみを持つ制約付き項書換え系のパターン除去に基づく変換を提案し，この変換が十分完全性や最内停止性などの性質に関して等価変換となる十分条件を示す．また，変換の応用として書換え完全性の判定法を提案する．

記述言語：日本語  

記述言語：日本語  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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

記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

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.

記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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.

記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

担当区分：筆頭著者   記述言語：英語  

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

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

記述言語：日本語  

記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

記述言語：日本語  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語  

記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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

担当区分：筆頭著者   記述言語：英語  

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

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：英語  

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.

記述言語：日本語  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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.

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

帰納的定理の証明原理の1 つである潜在帰納法が制約付き項書換え系に対応するよ
うに拡張され，命令型プログラムの等価性検証に応用されている．本論文では，別の
証明原理である書換え帰納法を制約付き項書き換え系に対応するように拡張するとと
もに，その正しさを証明する．また，拡張された書換え帰納法に基づいた帰納的定理
の証明法を提案する．さらに，帰納的定理でないことを示す反証の手法についても議
論する．

記述言語：日本語  

記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

手続き型プログラムの検証手法として，モデル検査やホーア論理に基づく検証手法
が代表的である．一方，項書換えの分野では帰納的定理の証明手法として潜在帰納法
や書換え帰納法などが広く研究されている．本論文では，帰納的定理の証明法を利用
して手続き型プログラムの等価性の検証を試みる．具体的には，自然数上のwhile 言
語で定義された手続き型関数からプレスブルガー文を規則の制約として持つことが許
された制約付き項書換え系への変換を与え，その変換により手続き型プログラムの等
価性を書換え系の関数の等価性に帰着させ，潜在帰納法を用いて等価性検証を試みる．
この手法を実現するために，合流性を保証するための危険対定理および完備化手続き
を制約付き書換えに対応するように拡張する．

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：日本語  

記述言語：日本語  

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

記述言語：日本語  

記述言語：日本語  

記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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.

記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

記述言語：日本語  

記述言語：英語  

記述言語：英語  

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

担当区分：筆頭著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：英語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語  

担当区分：筆頭著者   記述言語：日本語  

開催年月日： 2022年7月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Haifa, Israel   国名：イスラエル国  

As a transformational approach, inversion is formulated in several settings, and the basic ideas are naive and similar. To generate a better form, e.g., non-overlapping systems if possible, determinization is used as a post-process of inversion for injective functions, and is the most challenging part in developing an inversion framework. In this talk, I introduce a framework of inversion and determinization in term rewriting. First, I explain a direct inversion of deterministic CTRSs, and a direct MSV-based determinization. Next, I explain the framework proposed by Gluck and Kawabe, which uses context-free grammars as intermediate representations of CTRSs. Finally, I explain a framework based on context-free expressions.

開催年月日： 2022年2月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：hybrid (Nagoya University / onlien)   国名：日本国  

開催年月日： 2021年9月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：online   国名：日本国  

開催年月日： 2021年3月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：online   国名：日本国  

開催年月日： 2019年2月 - 2019年3月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Ikaho, Gunma   国名：日本国  

開催年月日： 2018年9月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Ikaho, Gunma   国名：日本国  

開催年月日： 2018年3月

記述言語：日本語   会議種別：ポスター発表  

開催地：皆生グランドホテル天水   国名：日本国  

組合せ最適化問題は様々な分野に応用できるが，効率良く解くためには専門知識を必要とするという問題がある．本研究では，組合せ最適化問題を簡潔に記述できなおかつ効率的に解くことができるシステムの構築を目指して，理論的な枠組として関係の集合上に拡張した関係代数を提案し，それに基づく拡張SQL構文とその汎用ソルバによる解法を議論する．

開催年月日： 2018年3月

記述言語：日本語   会議種別：ポスター発表  

開催地：皆生グランドホテル天水   国名：日本国  

難解プログラミング言語とは意図的に読解が困難になるように設計された言語であり、中でも難解な言語としてMalbolgeがある。現在では低級アセンブリ言語と制御付き疑似命令列を経てC言語に制限を設けた高級言語からのコンパイラが実現されている。しかしこの高級言語では配列を扱うことができず、複雑なプログラムが書けなかった。本研究では配列を含む高級言語を処理してMalbolgeへ変換する手法を実装した。この変換にはメモリの空き領域をスタックとして用いることで実現した。

開催年月日： 2017年9月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Matsue, Shimane   国名：日本国  

開催年月日： 2017年2月 - 2017年3月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Shinojima, Aichi   国名：日本国  

開催年月日： 2016年9月

記述言語：英語   会議種別：口頭発表（一般）  

国名：オーストリア共和国  

開催年月日： 2014年9月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Jozankei, Sapporo   国名：日本国  

開催年月日： 2014年3月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2014年3月

記述言語：英語  

国名：デンマーク王国  

開催年月日： 2013年7月

記述言語：英語   会議種別：口頭発表（招待・特別）  

国名：ドイツ連邦共和国  

In this talk, we introduce an automated theorem proving method based on rewriting induction of constrained TRSs, and show how to apply it to the verification of C programs over integers. Especially, we show a technique to automatically generate (a candidate of) lamma equations that are necessary for the proof.

開催年月日： 2012年11月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2012年10月

記述言語：英語   会議種別：口頭発表（一般）  

国名：オーストリア共和国  

In this talk, I present two principles of program inversion
in term rewriting setting, a classical one and another one for tail
recursion. Rewrite rules generated by inversion methods based on the
principles are often non-deterministic w.r.t. application of rules to
redexes even if given functions are injective. For this reason,
determinization of inverted programs is one of the most challenging
topics in program inversion of injective functions. To make inverted
programs deterministic, I present an MSV transformation of term
rewriting systems, which converts a rewrite system to a more specific
version. The notion of MSV originated from the context of logic
programs.

開催年月日： 2011年12月

記述言語：英語   会議種別：口頭発表（招待・特別）  

国名：スペイン  

開催年月日： 2011年9月

記述言語：日本語   会議種別：ポスター発表  

開催地：沖縄産業支援センター   国名：日本国  

開催年月日： 2011年9月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2011年9月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2011年3月

記述言語：日本語   会議種別：ポスター発表  

開催地：定山渓ビューホテル   国名：日本国  

開催年月日： 2011年3月

記述言語：日本語   会議種別：ポスター発表  

開催地：定山渓ビューホテル   国名：日本国  

開催年月日： 2011年3月

記述言語：日本語   会議種別：ポスター発表  

開催地：定山渓ビューホテル   国名：日本国  

開催年月日： 2011年2月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2010年3月

記述言語：日本語   会議種別：ポスター発表  

国名：日本国  

開催年月日： 2010年3月

記述言語：日本語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2010年2月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2009年9月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2009年9月

記述言語：日本語   会議種別：ポスター発表  

国名：日本国  

開催年月日： 2008年3月

記述言語：日本語  

国名：日本国  

開催年月日： 2007年8月

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2007年2月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2006年9月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2006年2月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2005年8月

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2004年11月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2004年10月

記述言語：英語   会議種別：口頭発表（招待・特別）  

国名：日本国  

開催年月日： 2004年4月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2003年9月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2003年3月

記述言語：英語   会議種別：口頭発表（一般）  

国名：日本国  

開催年月日： 2002年10月

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2002年3月

記述言語：英語   会議種別：口頭発表（一般）