Towards More Precise Rewriting Approximations

Yohan Boichut (1) , Jacques Chabin (1) , Pierre Réty (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.Their success highly depends on the quality of the approximation. 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 on the one hand, using synchronized tree languages 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, whereas the former techniques compute a strict over-approximation.

Mots clés: tree languages; term rewriting; logic programming; reachability

Domaines: Informatique et langage [cs.CL]

Yohan Boichut, Jacques Chabin, Pierre Réty. Towards More Precise Rewriting Approximations. Proceedings of Language and Automata Theory and Applications (LATA), Mar 2015, Nice, France. ⟨hal-01135918⟩