Some undecidability results for weakly confluent monadic string-rewriting systems

Abstract

For a finite weakly confluent monadic string-rewriting system R presenting a group the set of valid linear sentences is decidable. Thus, many decision problems for R can be solved in a uniform way. Here we show that this is no longer true in general if R is a finite weakly confluent monadic string-rewriting system that does not present a group. In fact, we construct a system R of this form that has an undecidable word problem. Some additional undecidability results as well as some decidability results for finite weakly confluent monadic string-rewriting systems are also presented.