A Polynomial Algorithm Testing Partial Confluence of Basic Semi-Thue Systems

Algorithms and Reductions for Rewriting Problems

In this paper we initiate a study of polynomial-time reductions for some basic decision problems of rewrite systems. We then give a polynomial-time algorithm for the unique-normal-form property of ground systems for the first time. Next we prove undecidability of several problems for a fixed string rewriting system using our reductions. Finally, we prove the decidability of confluence for commu...

Complexity Results for Confluence Problems

We study the complexity of the confluence problem for restricted kinds of semi–Thue systems, vector replacement systems and general trace rewriting systems. We prove that confluence for length– reducing semi–Thue systems is P–complete and that this complexity reduces to NC in the monadic case. For length–reducing vector replacement systems we prove that the confluence problem is PSPACE– complet...

Confluence of Length Preserving String Rewriting Systems is Undecidable

Confluence that ensures the uniqueness of results of computation is one of important properties on rewriting systems. In this paper, we show undecidability of confluence for length preserving string rewriting systems (SRSs) and prove it by reducing the Post’s correspondence problem (PCP), which is known to be undecidable, to confluence problem of length preserving string rewriting systems. More...

Word Problems and Confluence Problems for Restricted Semi-Thue Systems

On String Rewriting Systems

String rewriting systems, also known as semi-Thue systems, consist of a set of rules l → r, specifying valid replacements of substrings of strings over a given alphabet. In the case of one single rule, it is an open problem whether there is a system that is neither terminating nor looping. Another open question is the decidability of termination. Difficulties arise especially for non-confluent ...