Unification Modulo ACUI Plus Distributivity Axioms

Anantharaman, Siva; Narendran, Paliath; Rusinowitch, Michaël

doi:10.1007/s10817-004-2279-7

Cited by 10 publications

(12 citation statements)

References 20 publications

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“…The exclusive-or symbol is ⊕ and the symbols pk and sk are used for public and private key encryption, respectively. This equational theory is useful for protocol verification (see [36]) and it is relevant here because there are no unification procedures available in the literature which are directly applicable to it, e.g., unification algorithms for exclusive-or such as [5] do not directly apply when extra equations are added. …”

Section: Examplementioning

confidence: 99%

Folding variant narrowing and optimal variant termination

Escobar

Sasse

Meseguer

2012

The Journal of Logic and Algebraic Programming

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If a set of equations E∪Ax is such that E is confluent, terminating , and coherent modulo Ax, narrowing with E modulo Ax provides a complete E ∪Ax-unification algorithm. However, except for the hopelessly inefficient case of full narrowing, nothing seems to be known about effective narrowing strategies in the general modulo case beyond the quite depressing observation that basic narrowing is incomplete modulo AC. In this work we propose an effective strategy based on the idea of the E ∪ Ax-variants of a term that we call folding variant narrowing. This strategy is complete, both for computing E ∪ Ax-unifiers and for computing a minimal complete set of variants for any input term. And it is optimally variant terminating in the sense of terminating for an input term t iff t has a finite, complete set of variants. The applications of folding variant narrowing go beyond providing a complete E ∪ Ax-unification algorithm: computing the E ∪Ax-variants of a term may be just as important as computing E ∪Ax-unifiers in recent applications of folding variant narrowing such as termination methods modulo axioms, and checking confluence and coherence of rules modulo axioms.

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Section: Examplementioning

confidence: 99%

Folding variant narrowing and optimal variant termination

Escobar

Sasse

Meseguer

2012

The Journal of Logic and Algebraic Programming

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“…This equational theory is relevant because there are no unification procedures directly applicable to it, e.g. unification algorithms for exclusive-or such as [3] do not directly apply if extra equations are added. The exclusive or symbol ⊕ has associative and commutative (AC) properties with 0 as its unit.…”

Section: Definition 6 (Ax-equalitymentioning

confidence: 99%

Folding Variant Narrowing and Optimal Variant Termination

Escobar

Sasse

Meseguer

2010

Rewriting Logic and Its Applications

137

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Abstract. If a set of equations E∪Ax is such that E is confluent, terminating, and coherent modulo Ax, narrowing with E modulo Ax provides a complete E ∪Ax-unification algorithm. However, except for the hopelessly inefficient case of full narrowing, nothing seems to be known about effective narrowing strategies in the general modulo case beyond the quite depressing observation that basic narrowing is incomplete modulo AC. In this work we propose an effective strategy based on the idea of the E ∪ Ax-variants of a term that we call folding variant narrowing. This strategy is complete, both for computing E ∪ Ax-unifiers and for computing a minimal complete set of variants for any input term. And it is optimally variant terminating in the sense of terminating for an input term t iff t has a finite, complete set of variants. The applications of folding variant narrowing go beyond providing a complete E ∪ Axunification algorithm: computing the E ∪Ax-variants of a term may be just as important as computing E ∪Ax-unifiers in recent applications of folding variant narrowing such as termination methods modulo axioms, and checking confluence and coherence of rules modulo axioms.

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“…There are mainly two 17 The fact that an equational theory T does not have a nitary narrowing-based algorithm does not by itself preclude the existence of a nitary unication algorithm obtained by other methods. In fact, the homomorphic theory we have just described does have a nitary unication algorithm [2]; however this dedicated unication algorithm is not an instance of a generic narrowing-based algorithm. However, as already explained, in the Maude-NPA the theories for which nitary unication is currently supported are either order-sorted theories with built-in axioms of commutativity and associativity-commutativity, or theories modulo such built-in axioms that are conuent, terminating, and coherent modulo Ax, and that are also strongly right irreducible.…”

Section: State Space Reduction Techniquesmentioning

confidence: 99%

“…As pointed out in Section 5.2, Rules of type (5) allow the dynamic introduction of new strands. However, new strands can also be introduced by unication of a state containing a variable denoting a set of strands and one of the Rules (1), (2), and (4), where variables v and v H denoting lists of input/output messages will be introduced by instantiation of . The same can happen with new intruder facts of the form ( inI), where is a variable.…”

Section: Limiting Dynamic Introduction Of New Strandsmentioning

confidence: 99%