Finer is better: Abstraction Refinement for Rewriting Approximations

International audienceTerm 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