Foundations of Software Science and Computation Structures

Volume 2987 of the series Lecture Notes in Computer Science pp 378-392

On Term Rewriting Systems Having a Rational Derivation

  • Antoine MeyerAffiliated withIrisa, campus de Beaulieu, Rennes Liafa, Université de Paris 7


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.