On s-regular preffix-rewriting systems and automatic structures

Authors:
Friedrich Otto
Affiliations:
Fachbereich Mathematik/Informatik, Universität Kassel, Kassel, Germany
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

Underlying the notion of an automatic structure is that of a synchronously regular (s-regular for short) set of pairs of strings. Accordingly we consider s-regular prefix-rewriting systems showing that even for fairly restricted systems of this form confluence is undecidable in general. Then a close correspondence is established between the existence of an automatic structure that yields a prefix-closed set of unique representatives for a finitely generated monoid and the existence of an s-regular canonical prefix-rewriting system presenting that monoid.