Match-Bounded String Rewriting Systems

Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

doi:10.1007/s00200-004-0162-8

Cited by 42 publications

(19 citation statements)

References 26 publications

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“…On the other hand, the tools AProVE, T T T 2 , NaTT, and MU-TERM participated in categories for many different variants of term rewrite systems. To prove termination of TRSs, the tools use both classical reduction orderings as well as more recent powerful improvements like dependency pairs [3], matrix interpretations [20], match-bounds [26], etc. To generate the required orderings automatically, the tools typically apply existing SAT and SMT solvers.…”

Section: Termination Of Rewritingmentioning

confidence: 99%

The Termination and Complexity Competition

Giesl

Rubio

Sternagel

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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The termination and complexity competition (termCOMP) focuses on automated termination and complexity analysis for various kinds of programming paradigms, including categories for term rewriting, integer transition systems, imperative programming, logic programming, and functional programming. In all categories, the competition also welcomes the participation of tools providing certifiable output. The goal of the competition is to demonstrate the power and advances of the stateof-the-art tools in each of these areas.

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Section: Termination Of Rewritingmentioning

confidence: 99%

The Termination and Complexity Competition

Giesl

Rubio

Sternagel

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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“…In this way, we re-use states that occur in the derivations [7]. As the following example shows, the corresponding property does not hold for term rewriting.…”

Section: Constructing Compatible Automatamentioning

confidence: 99%

“…We have previously applied this method to string rewriting [7]. The string rewriting version is implemented in the tools TORPA [18], Matchbox [17] and AProVE [11].…”

Section: Introductionmentioning

confidence: 99%

On tree automata that certify termination of left-linear term rewriting systems

Geser

Hofbauer²,

Waldmann

et al. 2007

Information and Computation

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We present a new method for proving termination of term rewriting systems automatically. It is a generalization of the match bound method for string rewriting. To prove that a term rewriting system terminates on a given regular language of terms, we first construct an enriched system over a new signature that simulates the original derivations. The enriched system is an infinite system over an infinite signature, but it is locally terminating: every restriction of the enriched system to a finite signature is terminating. We then construct iteratively a finite tree automaton that accepts the enriched given regular language and is closed under rewriting modulo the enriched system. If this procedure stops, then the enriched system is compact: every enriched derivation involves only a finite signature. Therefore, the original system terminates. We present three methods to construct the enrichment: top heights, roof heights, and match heights. Top and roof heights work for left-linear systems, while match heights give a powerful method for linear systems. For linear systems, the method is strengthened further by a forward closure construction. Using these methods, we give examples for automated termination proofs that cannot be obtained by standard methods.

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“…In this context, some families of rewrite systems have been identified as preserving rational languages (C 1 = C 2 = RAT) like k-period expanding systems ( [Leu08]), deleting systems ( [HW04]) and match-bounded systems ( [GHW04]) or preserving context-free languages (C 1 = C 2 = CF) like systems with inhibitor ( [McN01])and inverse match-bounded systems ( [GHW05]).…”

Section: Introductionmentioning

confidence: 99%

On prefixal one-rule string rewrite systems

Latteux

Roos

2019

Theoretical Computer Science

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Prefixal one-rule string rewrite systems are one-rule string rewrite systems for which the left-hand side of the rule is a prefix of the right-hand side of the rule. String rewrite systems induce a transformation over languages: from a starting word, one can associate all its descendants. We prove, in this work, that the transformation induced by a prefixal one-rule rewrite system always transforms a finite language into a context-free language, a property that is surprisingly not satisfied by arbitrary one-rule rewrite systems. We also give here a decidable characterization of the prefixal one-rule rewrite systems whose induced transformation is a rational transduction.

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Match-Bounded String Rewriting Systems

Cited by 42 publications

References 26 publications

The Termination and Complexity Competition

The Termination and Complexity Competition

On tree automata that certify termination of left-linear term rewriting systems

On prefixal one-rule string rewrite systems

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