On Term Rewriting Systems Having a Rational Derivation

Antoine Meyer (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to study the derivation relation of such systems (i.e. the reflexive and transitive closure of their rewriting relation) and, if possible, to provide a finite mechanism characterizing it. Using a notion of rational relations based on finite graph grammars, we show that the derivation of any bottom-up, top-down or suffix systems is rational, while it can be non recursive for prefix systems.

Domaines: Logique en informatique [cs.LO]

Antoine Meyer. On Term Rewriting Systems Having a Rational Derivation. FoSSaCS 2004, Mar 2004, Barcelona, Spain. pp.378-392, ⟨10.1007/b95995⟩. ⟨hal-00149816⟩