Feasible Trace Reconstruction for Rewriting Approximations

Yohan Boichut 1 Thomas Genet 2
1 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 Lande - Logiciel : ANalyse et DEveloppement
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
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 t can be shown by computing an overapproximation of the set of reachable terms and prove that t is not in the approximation. However, when the term t is in the approximation, nothing can be said. In this paper, we refine this approach and propose a method taking advantage of the approximation to compute a rewriting path to the reachable term when it exists, i.e. produce a counter example. The 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 of rewriting models.
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Submitted on : Friday, March 12, 2010 - 10:41:37 AM
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  • HAL Id : hal-00463426, version 1


Yohan Boichut, Thomas Genet. Feasible Trace Reconstruction for Rewriting Approximations. RTA'2006, Aug 2006, Seattle, United States. pp.123-135. ⟨hal-00463426⟩



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