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.
S. Escobar has been partially supported by the EU (FEDER) and the Spanish MEC under grant TIN2007-68093-C02-02, and Integrated Action HA 2006-0007. J. Meseguer and R. Sasse have been partially supported by the ONR Grant N00014-02-1-0715, and by the NSF Grants IIS 07-20482 and CNS 07-16638.
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Escobar, S., Meseguer, J., Sasse, R. (2008). Effectively Checking the Finite Variant Property . In: Voronkov, A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70590-1_6
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DOI: https://doi.org/10.1007/978-3-540-70590-1_6
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