About the descriptive power of certain classes of finite string-rewriting systems

Abstract

Finite string-rewriting systems can be used to present monoids and groups. In general, these finite presentations do not give much information about the monoids and groups presented. However, if we use finite systems that are canonical, then based on these systems we can effectively perform computations in the monoids and groups presented. Many decision problems that are undecidable in general can be solved with various degrees of complexity for various classes of finite canonical string-rewriting systems. Therefore, it is of interest to determine the descriptive power of these classes, i.e., to find algebraic characterizations for those classes of monoids that can be presented by certain types of finite canonical string-rewriting systems. So far most results in this area deal with the presentation of groups. Here we give a detailed overview over these results.