On Term Rewriting Systems Having a Rational Derivation

Details On Term Rewriting Systems Having a Rational Derivation On Term Rewriting Systems Having a Rational Derivation

2007-05-28

arxiv.org/abs/0705.4064v1

Foundations of Software Science and Computation Structures (05/03/2004) 378-392

Computer Science

Logic in Computer Science

Scientific paper

10.1007/b95995

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.

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