Algebraic Properties

Abstract

In this chapter we first review the notion in detail that string-rewriting systems can be seen as presentations of monoids. In particular, we will learn about the so-called Tietze transformations which are a means to change presentations without changing the monoid presented. Then we will address the following question: Given a finite string-rewriting system R on ∑, how much information on the algebraic structure of the monoid presented by (∑; R) can be obtained from R? We will establish a general undecidability result due to Markov and give some applications of it, before we finally derive some decidability results for presentations (∑; R), for which R satisfies certain additional restrictions, like being noetherian and confluent.