Regular Gröbner Bases

  title={Regular Gr{\"o}bner Bases},
  author={Jonas M{\aa}nsson and Patrik Nordbeck},
  journal={J. Symb. Comput.},
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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    Comput. Sci. J. Moldova
  • 2000
Algorithm to compute finite state automata which, given any rational language, recognize the languages of normal words and n-chains and can be used to compute the Hilbert series and Poincare series for any algebra with a rational set of leading words of its minimal Grobner basis.

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Some Undecidability Results Concerning the Property of Preserving Regularity

  • F. Otto
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  • 1998

A graded algebra with a non-rational Hilbert series