Regular Gröbner Bases

@article{Mnsson2002RegularGB,
  title={Regular Gr{\"o}bner Bases},
  author={Jonas M{\aa}nsson and Patrik Nordbeck},
  journal={J. Symb. Comput.},
  year={2002},
  volume={33},
  pages={163-181}
}
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. 

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