Regular Grobner bases

Abstract:
In this paper we introduce the concept of bi-automaton algebras, generalizing the automaton algebras previously defined by Ufnarovski. A bi-automaton algebra is a quotient of the free algebra, defined by a binomial ideal admitting a Grobner basis which can be encoded as a regular set; we call such a Grobner basis regular. We give several examples of bi-automaton algebras, and show how automata connected to regular Grobner bases can be used to perform reduction. (C) 2002 Academic Press.