Makanin's algorithm for word equations-two improvements and a generalization

Schulz, Klaus U.

doi:10.1007/3-540-55124-7_4

Cited by 74 publications

(61 citation statements)

References 4 publications

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“…Solvability of traversal equations is still an open question, but we prove that a variant of them (the so called rankand permutation-bounded traversal equations) can be reduced to word equations with regular constraints [Sch91], which are decidable. This reduction is somehow inspired in the reduction from trace equations to word equations used in [DMM97] to prove decidability of trace equations.…”

Section: Traversal Equationsmentioning

confidence: 98%

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Context Unification and Traversal Equations

Levy

Villaret

2001

Rewriting Techniques and Applications

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Abstract. Context unification was originally defined by H. Comon in ICALP'92, as the problem of finding a unifier for a set of equations containing first-order variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are second-order variables that are restricted to be instantiated by linear terms (a linear term is a λ-expression λx 1 · · · λxn . t where every xi occurs exactly once in t). In this paper, we prove that, if the so called rank-bound conjecture is true, then the context unification problem is decidable. This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints.

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Section: Traversal Equationsmentioning

confidence: 98%

“…We also introduce a new notion of traversal equation, noted t ≡ u, and meaning t and u are traversal sequences of the same term. We prove that a variant of these constraints can be reduced to word equations with regular constraints, that are decidable [Sch91].…”

Section: A Naive Reductionmentioning

confidence: 99%

Context Unification and Traversal Equations

Levy

Villaret

2001

Rewriting Techniques and Applications

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“…Makanin (see [15]) shows that the question whether an equation in a free monoid has a solution is decidable. It can be generalized in the way that existential first-order theory of equations in a free monoid with additional regular constraints on the variables is decidable [18]. For an overview of unification theory consult e.g.…”

Section: Introductionmentioning

confidence: 99%

Matching Modulo Associativity and Idempotency Is NP—Complete

Klíma¹,

Srba

2000

Lecture Notes in Computer Science

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“…Both problems are generalizations of Word Unification [7,13,22,26,30]. Word Unification is the problem of solving equations between terms build up from letters and word variables.…”

Section: Introductionmentioning

confidence: 99%

“…We prove that Left-Hole Context Unification is a decidable variant of Context Unification. We do it by reducing Left-Hole Context Unification to Word Unification with Regular Constraints that is known to be decidable [30]. The reduction transforms context equations into word equations on the postorder traversal of the terms.…”

Section: Introductionmentioning

confidence: 99%

Sequence Unification Through Currying

Kutsia

Levy

Villaret

Lecture Notes in Computer Science

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Abstract. Sequence variables play an interesting role in unification and matching when dealing with terms in an unranked signature. Sequence Unification generalizes Word Unification and seems to be appealing for information extraction in XML documents, program transformation, and rule-based programming.In this work we study a relation between Sequence Unification and another generalization of Word Unification: Context Unification. We introduce a variant of Context Unification, called Left-Hole Context Unification that serves us to reduce Sequence Unification to it: We define a partial currying procedure to translate sequence unification problems into left-hole context unification problems, and prove soundness of the translation. Furthermore, a precise characterization of the shape of the unifiers allows us to easily reduce Left-Hole Context Unification to (the decidable problem of) Word Unification with Regular Constraints, obtaining then a decidability proof for an extension of Sequence Unification.

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Makanin's algorithm for word equations-two improvements and a generalization

Cited by 74 publications

References 4 publications

Context Unification and Traversal Equations

Context Unification and Traversal Equations

Matching Modulo Associativity and Idempotency Is NP—Complete

Sequence Unification Through Currying

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