Disproving Confluence of Term Rewriting Systems by Interpretation and Ordering

Aoto, Takahito

doi:10.1007/978-3-642-40885-4_22

Cited by 10 publications

(19 citation statements)

References 27 publications

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“…We have shown the usefulness of this approach by an exhaustive consideration of examples from several recent papers addressing the role of infeasibility when applied to such problems. In particular, we could deal with all of Aoto's examples in [1] (regarding proofs of non-joinability of ground terms in TRSs), see Appendix B. In [17], Middeldorp uses different approximations to the estimation of the dependency graph for TRSs in the analysis of termination using dependency pairs.…”

Section: Discussionmentioning

confidence: 99%

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Use of logical models for proving infeasibility in term rewriting

Lucas

Gutiérrez

2018

Information Processing Letters

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Given a (Conditional) Rewrite System R and terms s and t, we consider the following problem: is there a substitution σ instantiating the variables in s and t such that the reachability test σ(s) → * R σ(t) succeeds? If such a substitution does not exist, we say that the problem is infeasible; otherwise, we call it feasible. Similarly, we can consider reducibility, involving a single rewriting step. In term rewriting, a number of important problems involve such infeasibility tests (e.g., confluence and termination analysis). We show how to recast infeasibility tests into the problem of finding a model of a set of (first-order) sentences representing the operational semantics of R together with some additional sentences representing the considered property which is formulated as an infeasibility test.

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Section: Discussionmentioning

confidence: 99%

“…This allows us to deal with more applications and examples. Interestingly, our semantic approach together with the aforementioned improvements applies to all the examples solved in papers developing different specific techniques to deal with problems (i)-(vii) [1,17,20,21].…”

Section: Introductionmentioning

confidence: 99%

Use of logical models for proving infeasibility in term rewriting

Lucas

Gutiérrez

2018

Information Processing Letters

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“…The former by joinability of critical pairs and the latter reusing all the available machinery for termination techniques. For nonconfluence CPF admits the syntactic criteria mentioned in [31], the tree-automata based techniques of [10], and the methods based on interpretations and orders of [1].…”

Section: Split the Input Trsmentioning

confidence: 99%

“…For these decisions, usually the person who wanted to add a new technique to CPF was asked to provide a proposal. This proposal was then integrated into a development version of CPF and put under discussion on the CPF mailing list 1. Comments during the discussion were integrated in the proposal, and after the discussion has stopped, the modified proposal was integrated into the official CPF version.…”

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confidence: 99%

The Certification Problem Format

Sternagel

Thiemann

2014

Electron. Proc. Theor. Comput. Sci.

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We provide an overview of CPF, the certification problem format, and explain some design decisions. Whereas CPF was originally invented to combine three different formats for termination proofs into a single one, in the meanwhile proofs for several other properties of term rewrite systems are also expressible: like confluence, complexity, and completion. As a consequence, the format is already supported by several tools and certifiers. Its acceptance is also demonstrated in international competitions: the certified tracks of both the termination and the confluence competition utilized CPF as exchange format between automated tools and trusted certifiers.

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“…2 In the recent past, several confluence results have been formalized, starting from the fundamental result by Knuth and Bendix [12] that a terminating rewrite system is confluent if and only if all its critical pairs are joinable. For nonterminating rewrite systems, weak orthogonality as well as sufficient conditions for non-joinability of critical pairs based on unification, discrimination pairs [1], interpretations, and tree automata [6] have been formalized. These results are described in [14].…”

Section: Introductionmentioning

confidence: 99%

Certification of Classical Confluence Results for Left-Linear Term Rewrite Systems

Nagele

Middeldorp

2016

Interactive Theorem Proving

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This paper presents the first formalization of three classic confluence criteria for first-order term rewrite systems by Huet and Toyama. We have formalized proofs, showing that (1) linear strongly closed systems, (2) left-linear parallel closed systems, and (3) left-linear almost parallel closed systems are confluent. The third result is extended to commutation. The proofs were carried out in the proof assistant Isabelle/HOL as part of the library IsaFoR and integrated into the certifier CeTA, significantly increasing the number of certifiable proofs produced by automatic confluence tools.

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Disproving Confluence of Term Rewriting Systems by Interpretation and Ordering

Cited by 10 publications

References 27 publications

Use of logical models for proving infeasibility in term rewriting

Use of logical models for proving infeasibility in term rewriting

The Certification Problem Format

Certification of Classical Confluence Results for Left-Linear Term Rewrite Systems

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