Thue systems as rewriting systems

Authors:
Ronald V. Book
Affiliations:
Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
Venue:
Journal of Symbolic Computation
Year:
1987

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Abstract

This paper is a survey of recent results on Thue systems, where the systems are viewed as rewriting systems on strings over a finite alphabet. The emphasis is on Thue systems with the Church-Rosser property, where the notion of reduction is based on length-decreasing rewriting rules. The main effort is expended in outlining the properties of such systems, paying close attention to the issue of the possible decidability of properties and to the issue of the computational complexity of decidable properties. Since Thue systems may also be considered as presentations of monoids, the language of monoids (and groups) is used to describe some of these properties.