Effectively Checking the Finite Variant Property

  • Authors:
  • Santiago Escobar;José Meseguer;Ralf Sasse

  • Affiliations:
  • Universidad Politécnica de Valencia, Spain;University of Illinois at Urbana-Champaign, USA;University of Illinois at Urbana-Champaign, USA

  • Venue:
  • RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
  • Year:
  • 2008

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Abstract

An equational theory decomposed into a set Bof equational axioms and a set Δof rewrite rules has the finite variant(FV) propertyin the sense of Comon-Lundh and Delaune iff for each term tthere is a finite set {t1,...,tn} of 驴Δ,B-normalized instances of tso that any instance of tnormalizes to an instance of some timodulo 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.