On the connections between rewriting and formal language theory

Abstract

Formal language theory, and in particular the theory of automata, has provided many tools that have been found extremely useful in rewriting theory, since automata can be used for deciding certain properties of rewriting systems as well as for constructing (weakly) confluent rewriting systems. On the other hand, rewriting theory has had some influence on the development of formal language theory, since based on certain rewriting systems some interesting classes of formal languages have been defined. Here a survey on some connections between rewriting and formal language theory is given, starting from the classical string languages and string-rewriting systems and continuing with tree automata and term-rewriting systems.