Automating the dependency pair method

Hirokawa, Nao; Middeldorp, Aart

doi:10.1016/j.ic.2004.10.004

Cited by 85 publications

(71 citation statements)

References 22 publications

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“…Similarly there is a decrease of 1 for the elementary cycle [14,15,14]. The two labeled graphs in Fig.…”

Section: From Cycles To Sccsmentioning

confidence: 83%

“…In general it is not computable but sound approximations exist [1,12,15,23]. Here soundness means that every edge in the original graph is also an edge in the estimated graph and hence it forms an over-approximation of the actual dependency graph.…”

Section: Dependency Pair Frameworkmentioning

confidence: 99%

“…Hence for the elementary cycle [13,14,15,13] the interpreted value decreases by 2 in every loop. Similarly there is a decrease of 1 for the elementary cycle [14,15,14].…”

Section: From Cycles To Sccsmentioning

confidence: 99%

“…The example above shows that this is no longer true for increasing interpretations. The problematic non-terminating sequence corresponds to a path [13,14,15,14,15,13] where the interpreted value is increased in the elementary cycle [14,15,14] and consequently the cost of [13,14,15,14,15,13] is zero and there is no decrease. Considering (infinitely many!)…”

Section: From Cycles To Sccsmentioning

confidence: 99%

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Increasing interpretations

Zankl

Middeldorp

2009

Ann Math Artif Intell

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The article at hand introduces a refinement of interpretation-based termination criteria for term rewrite systems in the dependency pair setting. Traditional methods share the property that-in order to be successful-all rewrite rules must (weakly) decrease with respect to some measure. One novelty of our approach is that we allow some rules to increase the interpreted value. These rules are found by simultaneously searching for adequate polynomial interpretations while considering the information of the dependency graph. We prove that our method extends the termination proving power of linear interpretations. Furthermore, this generalization perfectly fits the dependency pair framework which is implemented in virtually every termination prover dealing with term rewrite systems. We present two dependency pair processors for increasing interpretations. The novelty of the second one is that it can be used to eliminate single edges from the dependency graph.

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“…Similarly there is a decrease of 1 for the elementary cycle [14,15,14]. The two labeled graphs in Fig.…”

Section: From Cycles To Sccsmentioning

confidence: 83%

Section: Dependency Pair Frameworkmentioning

confidence: 99%

“…Hence for the elementary cycle [13,14,15,13] the interpreted value decreases by 2 in every loop. Similarly there is a decrease of 1 for the elementary cycle [14,15,14].…”

Section: From Cycles To Sccsmentioning

confidence: 99%

Section: From Cycles To Sccsmentioning

confidence: 99%

See 2 more Smart Citations

Increasing interpretations

Zankl

Middeldorp

2009

Ann Math Artif Intell

Self Cite

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“…Hence, to automate the argument filtering transformation, one needs a method to efficiently search for a suitable argument filtering. For the dependency pair approach, such methods were developed in [14,16]. We feel that these methods can also work well for the argument filtering transformation, but the same cannot be said for AFT Ci π because there are infinitely many C i .…”

Section: Corollary 58mentioning

confidence: 99%

Elimination Transformations for Associative–Commutative Rewriting Systems

2006

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In order to simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of elimination transformations based on the notion of dependency pairs. We first present a theorem that gives a general and essential property for elimination transformations, making them sound with ACtermination. Based on the theorem, we design an elimination transformation called the argument filtering transformation. Next, we clarify the relation among various elimination transformations by comparing them with a corresponding restricted 206 J Autom Reasoning (2006) 37:205-229 argument filtering transformation. Finally, we compare the AC-dependency pair method with the argument filtering transformation.

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Automated theorem proving

Plaisted

2014

WIRES Cognitive Science

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Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

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Automating the dependency pair method

Cited by 85 publications

References 22 publications

Increasing interpretations

Increasing interpretations

Elimination Transformations for Associative–Commutative Rewriting Systems

Automated theorem proving

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