Finer Is Better: Abstraction Refinement for Rewriting Approximations

  • Authors:

  • Yohan Boichut;Roméo Courbis;Pierre-Cyrille Héam;Olga Kouchnarenko

  • Affiliations:

  • INRIA/PAREO, Villers-Lès Nancy Cedex, F-54602;INRIA/CASSIS, LIFC / University of Franche-Comté, Besançon Cedex, F-25030;INRIA/CASSIS, LIFC / University of Franche-Comté, Besançon Cedex, F-25030;INRIA/CASSIS, LIFC / University of Franche-Comté, Besançon Cedex, F-25030

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

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Abstract

Term rewriting systems are now commonly used as a modeling language for programs or systems. On those rewriting based models, reachability analysis, i.e. proving or disproving that a given term is reachable from a set of input terms, provides an efficient verification technique. For disproving reachability (i.e. proving non reachability of a term) on non terminating and non confluent rewriting models, Knuth-Bendix completion and other usual rewriting techniques do not apply. Using the tree automaton completion technique, it has been shown that the non reachability of a term tcan be shown by computing an over-approximation of the set of reachable terms and prove that tis not in the over-approximation. However, when the term tis in the approximation, nothing can be said.In this paper, we improve this approach as follows: given a term t, we try to compute an over-approximation which does not contain tby using an approximation refinement that we propose. If the approximation refinement fails then tis a reachable term. This semi-algorithm has been prototyped in the Timbuk tool. We present some experiments with this prototype showing the interest of such an approach w.r.t. verification on rewriting models.