Multi-completion with Termination Tools (System Description)

Sato, Hiroki; Winkler, Sarah; Kurihara, Masahito; Middeldorp, Aart

doi:10.1007/978-3-540-71070-7_26

Cited by 12 publications

(12 citation statements)

References 7 publications

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“…Multi-completion with termination tools [21,22,36] constitutes a combination of these two approaches. While the use of termination tools allows for automatic completion without user interaction, multi-completion enables to keep track of multiple combinations of orientations in parallel, thereby exploiting sharing for efficiency reasons.…”

Section: Introductionmentioning

confidence: 99%

“…The implementation of our technique thus yields a powerful tool for automatic completion with a high flexibility concerning orientations. In this paper we describe the underlying inference system, and present simulation and correctness results along with the proofs that were omitted in [21,22] due to reasons of space. After detecting a flaw in the fairness definition of [15], we newly contribute a corrected and explicit definition for MKBtt.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Completion with Termination Tools

et al. 2012

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Knuth-Bendix completion is a classical calculus in automated deduction for transforming a set of equations into a confluent and terminating set of directed equations which can be used to decide the induced equational theory. Multicompletion with termination tools constitutes an approach that differs from the classical method in two respects: (1) external termination tools replace the reduction order-a typically critical parameter-as proposed by , and (2) multi-completion as introduced by Kurihara and Kondo (1999) is used to keep track of multiple orientations in parallel while exploiting sharing to boost efficiency. In this paper we describe the inference system, give the full proof of its correctness and comment on completeness issues. Critical pair criteria and isomorphisms are presented as refinements together with all proofs. We furthermore describe the implementation of our approach in the tool mkbTT, present extensive experimental results and report on new completions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-Completion with Termination Tools

et al. 2012

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“…In this paper, we present a new variant of rewriting induction procedures, called multi-context rewriting induction (MRIt), based on the idea of the multi-completion [15], [18], [19]. Our procedure efficiently simulates execution of parallel RIt processes in a single process.…”

Section: Introductionmentioning

confidence: 99%

Multi-Context Rewriting Induction with Termination Checkers

Sato

Kurihara

2010

IEICE Trans. Inf. & Syst.

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SUMMARYInductive theorem proving plays an important role in the field of formal verification of systems. The rewriting induction (RI) is a method for inductive theorem proving proposed by Reddy. In order to obtain successful proofs, it is very important to choose appropriate contexts (such as in which direction each equation should be oriented) when applying RI inference rules. If the choice is not appropriate, the procedure may diverge or the users have to come up with several lemmas to prove together with the main theorem. Therefore we have a good reason to consider parallel execution of several instances of the rewriting induction procedure, each in charge of a distinguished single context in search of a successful proof. In this paper, we propose a new procedure, called multicontext rewriting induction, which efficiently simulates parallel execution of rewriting induction procedures in a single process, based on the idea of the multi-completion procedure. By the experiments with a well-known problem set, we discuss the effectiveness of the proposed procedure when searching along various contexts for a successful inductive proof.

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“…From the results, we can see that the node-based techniques of MKBdp and the caching are effective for improving the performance of MKBcs/POL, especially for the problems that require a long CPU time and a large number of processes such as WSW07 CGE 3 and WS06 PR. A more practical implementation of MKBcs is outlined in our short, system description paper [13]. There is some overlap between the current paper and [13], such as a basic description of MKBcs and a part of experiments, but in [13], the authors introduced the idea of MKBcs only informally and briefly (without proofs and examples) and, instead, described the implementation extensively.…”

Section: Evaluation Of Mkbdp and Cachingmentioning

confidence: 99%

Constraint-Based Multi-Completion Procedures for Term Rewriting Systems

Sato¹,

Kurihara²,

Winkler

et al. 2009

IEICE Trans. Inf. & Syst.

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SUMMARYIn equational theorem proving, convergent term rewriting systems play a crucial role. In order to compute convergent term rewriting systems, the standard completion procedure (KB) was proposed by Knuth and Bendix and has been improved in various ways. The multi-completion system MKB developed by Kurihara and Kondo accepts as input a set of reduction orders in addition to equations and efficiently simulates parallel processes each of which executes the KB procedure with one of the given orderings. Wehrman and Stump also developed a new variant of completion procedure, constraint-based completion, in which reduction orders need not be given by using automated modern termination checkers. As a result, the constraint-based procedures simulate the execution of parallel KB processes in a sequential way, but naive search algorithms sometimes cause serious inefficiency when the number of the potential reduction orders is large. In this paper, we present a new procedure, called a constraint-based multi-completion procedure MKBcs, by augmenting the constraint-based completion with the framework of the multi-completion for suppressing the combinatorial explosion by sharing inferences among the processes. The existing constraint-based system Slothrop, which basically employs the best-first search, is more efficient when its built-in heuristics for process selection are appropriate, but when they are not, our system is more efficient. Therefore, both systems have their role to play.

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Multi-completion with Termination Tools (System Description)

Cited by 12 publications

References 7 publications

Multi-Completion with Termination Tools

Multi-Completion with Termination Tools

Multi-Context Rewriting Induction with Termination Checkers

Constraint-Based Multi-Completion Procedures for Term Rewriting Systems

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