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The finite variant property: How to get rid of some algebraic properties

By Hubert Comon-lundh, Stéphanie Delaune and France Télécom R

Abstract

Abstract. We consider the following problem: Given a term t, a rewrite system R, a finite set of equations E ′ such that R is E ′-convergent, com-pute finitely many instances of t: t1,..., tn such that, for every substi-tution σ, there is an index i and a substitution θ such that tσ ↓ =E ′ tiθ (where tσ ↓ is the normal form of tσ w.r.t. →E ′ \R). The goal of this paper is to give equivalent (resp. sufficient) conditions for the finite variant property and to systematically investigate this property for equational theories, which are relevant to security protocols verification. For instance, we prove that the finite variant property holds for Abelian Groups, and a theory of modular exponentiation and does not hold for the theory ACUNh (Associativity, Commutativity, Unit, Nilpotence, homomorphism)

Publisher: Springer
Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.1999
Provided by: CiteSeerX
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