Match-Bounded String Rewriting Systems

Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

doi:10.1007/978-3-540-45138-9_39

Cited by 20 publications

(29 citation statements)

References 15 publications

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“…We further show that failure of the method is not completely characterized by the presence of a so-called witnessing set. Both results settle open problems in [7].…”

Section: Introductionsupporting

confidence: 79%

“…When c is not fixed, match-boundedness becomes undecidable. This settles an open problem in [7]. 4 Theorem 33.…”

Section: Two Results For Match-bounded String Rewritingmentioning

confidence: 85%

“…One of these is regularity preservingness [7]. The following result of [7] states that match-boundedness is decidable if the bound c is fixed.…”

Section: Two Results For Match-bounded String Rewritingmentioning

confidence: 99%

“…General knowledge of the match-bound technique [7,10] will be helpful. Below we recall important definitions and results from the latter paper.…”

Section: Preliminariesmentioning

confidence: 99%

“…Initially proposed for string rewriting by Geser, Hofbauer, and Waldmann [7], the method has recently been extended to left-linear term rewrite systems [10]. Variations and improvements are discussed in [5,8,9].…”

Section: Introductionmentioning

confidence: 99%

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Proving Termination of Rewrite Systems Using Bounds

Korp

Middeldorp

Lecture Notes in Computer Science

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Abstract. The use of automata techniques to prove the termination of string rewrite systems and left-linear term rewrite systems is advocated by Geser et al. in a recent sequence of papers. We extend their work to non-left-linear rewrite systems. The key to this extension is the introduction of so-called raise rules and the use of tree automata that are not quite deterministic. Furthermore, we present negative solutions to two open problems related to string rewrite systems.

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“…We further show that failure of the method is not completely characterized by the presence of a so-called witnessing set. Both results settle open problems in [7].…”

Section: Introductionsupporting

confidence: 79%

“…When c is not fixed, match-boundedness becomes undecidable. This settles an open problem in [7]. 4 Theorem 33.…”

Section: Two Results For Match-bounded String Rewritingmentioning

confidence: 85%

“…One of these is regularity preservingness [7]. The following result of [7] states that match-boundedness is decidable if the bound c is fixed.…”

Section: Two Results For Match-bounded String Rewritingmentioning

confidence: 99%

“…General knowledge of the match-bound technique [7,10] will be helpful. Below we recall important definitions and results from the latter paper.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proving Termination of Rewrite Systems Using Bounds

Korp

Middeldorp

Lecture Notes in Computer Science

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AProVE 1.2: Automatic Termination Proofs in the Dependency Pair Framework

Giesl

Schneider–Kamp

Thiemann

2006

Automated Reasoning

191

245

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Termination of Cycle Rewriting

Zantema

König

Bruggink

2014

Lecture Notes in Computer Science

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String rewriting can not only be applied on strings, but also on cycles and even on general graphs. In this paper we investigate termination of string rewriting applied on cycles, shortly denoted as cycle rewriting, which is a strictly stronger requirement than termination on strings. Most techniques for proving termination of string rewriting fail for proving termination of cycle rewriting, but match bounds, arctic matrices and tropical matrices can be applied. Further we show how any terminating string rewriting system can be transformed to a terminating cycle rewriting system, preserving derivational complexity.

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Match-Bounded String Rewriting Systems

Cited by 20 publications

References 15 publications

Proving Termination of Rewrite Systems Using Bounds

Proving Termination of Rewrite Systems Using Bounds

AProVE 1.2: Automatic Termination Proofs in the Dependency Pair Framework

Termination of Cycle Rewriting

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