Effectively Checking the Finite Variant Property

  • Santiago Escobar
  • José Meseguer
  • Ralf Sasse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5117)

Abstract

An equational theory decomposed into a set B of equational axioms and a set Δ of rewrite rules has the finite variant (FV) property in the sense of Comon-Lundh and Delaune iff for each term t there is a finite set {t 1,...,t n } of →Δ,B-normalized instances of t so that any instance of t normalizes to an instance of some t i modulo B. This is a very useful property for cryptographic protocol analysis, and for solving both unification and disunification problems. Yet, at present the property has to be established by hand, giving a separate mathematical proof for each given theory: no checking algorithms seem to be known. In this paper we give both a necessary and a sufficient condition for FV from which we derive an algorithm ensuring the sufficient condition, and thus FV. This algorithm can check automatically a number of examples of FV known in the literature.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Santiago Escobar
    • 1
  • José Meseguer
    • 2
  • Ralf Sasse
    • 2
  1. 1.Universidad Politécnica de ValenciaSpain
  2. 2.University of Illinois at Urbana-ChampaignUSA

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