Towards an Efficient Implementation of Tree Automata Completion

  • Authors:
  • Emilie Balland;Yohan Boichut;Thomas Genet;Pierre-Etienne Moreau

  • Affiliations:
  • Loria, INRIA Nancy --- Grand Est, France;Loria, INRIA Nancy --- Grand Est, France;Irisa, INRIA Rennes-Bretagne Atlantique, France;Loria, INRIA Nancy --- Grand Est, France

  • Venue:
  • AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
  • Year:
  • 2008

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Abstract

Term Rewriting Systems (TRSs) are now commonly used as a modeling language for applications. In 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. Using a tree automata completion technique, it has been shown that the non reachability of a term tcan be verified by computing an over-approximation of the set of reachable terms and proving that tis not in the over-approximation. Since the verification of real programs gives rise to rewrite models of significant size, efficient implementations of completion are essential. We present in this paper a TRS transformation preserving the reachability analysis by tree automata completion. This transformation makes the completion implementation based on rewriting techniques possible. Thus, the reduction of a term to a state by a tree automaton is fully handled by rewriting. This approach has been prototyped in Tom, a language extension which adds rewriting primitives to Java. The first experiments are very promising relative to the state-of-the-art tool Timbuk.