Towards more precise rewriting approximations

Abstract

To check a system, some verification techniques consider a set of terms I that represents the initial configurations of the system, and a rewrite system R that represents the system behavior. To check that no undesirable configuration is reached, they compute an over-approximation of the set of descendants (successors) issued from I by R, expressed by a tree language. Some techniques have been presented using regular tree languages, and more recently using non-regular languages to get better approximations: using context-free tree languages [1] on the one hand, using synchronized tree languages [2] on the other hand. In this paper, we merge these two approaches to get even better approximations: we compute an over-approximation of the descendants, using synchronized-context-free tree languages expressed by logic programs. We give several examples for which our procedure computes the descendants in an exact way, unlike former techniques.