Finite and infinite regular thue systems

This dissertation studies certain classes of Thue system, concentrating on the Church-Rosser property. The following new results are obtained about infinite regular Thue systems S: (1) if S is Church-Rosser, the word problem is solvable in linear time; (2) if S is monadic Church-Rosser, it defines a nontrivial boolean algebra of DCFLs; (3) if S is monadic Church-Rosser and so is another system T, equivalence of S and T is decidable; (4) if S is monadic, it is decidable if S is Church-Rosser; (5) if S is not monadic it is undecidable if S is Church-Rosser. The following new results are obtained about finite Thue systems S: (1) it is undecidable if there exists another finite Thue system T which is equivalent to S and is Church-Rosser (respectively: almost confluent, preperfect); (2) it is undecidable if S generates a Church-Rosser congruence. Some of these results generalise results about finite Thue systems, and some answer what had previously been open questions. The results are obtained using the theories of automata and formal languages, of Turing machines, and of finitely presented groups.