Basic Syntactic Mutation

Lynch, Christopher; Morawska, Barbara

doi:10.1007/3-540-45620-1_37

Cited by 16 publications

(26 citation statements)

References 11 publications

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“…Inspired by Basic Syntactic Mutation [5,14], we explored forward closure and its relation to the finite variant property [6]. We found that, with suitable redundancy constraints, the finiteness of forward closure is equivalent to the finite variant property.…”

Section: Discussionmentioning

confidence: 99%

“…An instance is ground if its terms do not contain any variables. A ground equation e is strictly redundant in E if and only if it is a consequence of equations in Gr (E) which are smaller than e modulo the ordering we use to show termination [14]. An equation e is strictly redundant in E if and only if every ground instance e of e is strictly redundant in E. In our setting, with convergent rewriting systems R and reduction orderings , this can be formulated as follows.…”

Section: Strict Redundancymentioning

confidence: 99%

“…Two important syntactic paradigms have been developed to identify such instances. One paradigm was developed in "Basic Syntactic Mutation", by Christopher Lynch and Barbara Morawska [14]. They give syntactic criteria on equational axioms E which guarantee that the corresponding E-unification problem is in NP.…”

Section: Introductionmentioning

confidence: 99%

“…Unification modulo a convergent term rewrite system is undecidable, even with just a single rule. To identify decidable (and tractable) cases, two paradigms have been developed -Basic Syntactic Mutation [14] and the Finite Variant Property [6]. Inspired by the Basic Syntactic Mutation approach, we investigate the notion of forward closure along with suitable redundancy constraints.…”

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confidence: 99%

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On Forward Closure and the Finite Variant Property

Bouchard

Gero

Lynch

et al. 2013

Frontiers of Combining Systems

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Abstract. Equational unification is an important research area with many applications, such as cryptographic protocol analysis. Unification modulo a convergent term rewrite system is undecidable, even with just a single rule. To identify decidable (and tractable) cases, two paradigms have been developed -Basic Syntactic Mutation [14] and the Finite Variant Property [6]. Inspired by the Basic Syntactic Mutation approach, we investigate the notion of forward closure along with suitable redundancy constraints. We show that a convergent term rewriting system R has a finite forward closure if and only if R has the finite variant property. We also show the undecidability of the finiteness of forward closure, therefore determining if a system has the finite variant property is undecidable.

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Section: Discussionmentioning

confidence: 99%

Section: Strict Redundancymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On Forward Closure and the Finite Variant Property

Bouchard

Gero

Lynch

et al. 2013

Frontiers of Combining Systems

Self Cite

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“…Even in cases where it is decidable, it is often of high complexity. In their seminal paper "Basic Syntactic Mutation" [7] Christopher Lynch and Barbara Morawska present syntactic criteria on equational axioms E that guarantee a polynomial time algorithm for the corresponding E-unification problem. As far as we know these are the only purely syntactic criteria that ensure a polynomial-time algorithm for unifiability.…”

Section: Introductionmentioning

confidence: 99%

Some Notes on Basic Syntactic Mutation

Gero¹,

Bouchard²,

Narendran³

EPiC Series in Computing

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Unification modulo convergent term rewrite systems is an important research area with many applications. In their seminal paper Lynch and Morawska gave three conditions on rewrite systems that guarantee that unifiability can be checked in polynomial time (P). We show that these conditions are tight, in the sense that relaxing any one of them will "upset the applecart," giving rise to unification problems that are not in P (unless P = NP), and in doing so address an open problem posed by Lynch and Morawska. We also investigate a related decision problem: we show the undecidability of subterm-collapse for the restricted term rewriting systems that we are considering.

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Rule-Based Unification in Combined Theories and the Finite Variant Property

Eeralla

Erbatur

Marshall

et al. 2019

Language and Automata Theory and Applications

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We investigate the unification problem in theories defined by rewrite systems which are both convergent and forward-closed. These theories are also known in the context of protocol analysis as theories with the finite variant property and admit a variant-based unification algorithm. In this paper, we present a new rule-based unification algorithm which can be seen as an alternative to the variant-based approach. In addition, we define forward-closed combination to capture the union of a forward-closed convergent rewrite system with another theory, such as the Associativity-Commutativity, whose function symbols may occur in right-hand sides of the rewrite system. Finally, we present a combination algorithm for this particular class of non-disjoint unions of theories.

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Basic Syntactic Mutation

Cited by 16 publications

References 11 publications

On Forward Closure and the Finite Variant Property

On Forward Closure and the Finite Variant Property

Some Notes on Basic Syntactic Mutation

Rule-Based Unification in Combined Theories and the Finite Variant Property

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