Finer is better: Abstraction Refinement for Rewriting Approximations

Yohan Boichut 1 Roméo Courbis 2, 3 Pierre-Cyrille Héam 2, 3 Olga Kouchnarenko 2, 3
1 PAREO - Formal islands: foundations and applications
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 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
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 over-approximation of the set of reachable terms and prove that t is not in the over-approximation. However, when the term t is 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 t by using an approximation refinement that we propose. If the approximation refinement fails then t is 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.
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Submitted on : Friday, February 4, 2011 - 9:04:04 PM
Last modification on : Friday, July 6, 2018 - 3:06:10 PM
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Yohan Boichut, Roméo Courbis, Pierre-Cyrille Héam, Olga Kouchnarenko. Finer is better: Abstraction Refinement for Rewriting Approximations. RTA'08, 19th international conference on Rewriting Techniques and Applications, Jul 2008, Hagenberg, Austria. pp.48--62, ⟨10.1007/978-3-540-70590-1⟩. ⟨hal-00563422⟩

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