Factorization of fuzzy automata

  • Authors:

  • Miroslav Ćirić;Aleksandar Stamenković;Jelena Ignjatović;Tatjana Petković

  • Affiliations:

  • Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia;Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia;Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia;Nokia, Salo, Finland

  • Venue:
  • FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
  • Year:
  • 2007

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Abstract

We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generalizations of recently studied right invariant or well-behaved equivalences on NFAs, and congruences on fuzzy automata. We give a procedure for constructing the greatest right invariant fuzzy equivalence contained in a given fuzzy equivalence, whichwork if the underlying structure of truth values is a locally finite residuated lattice.