An improved algorithm for determinization of weighted and fuzzy automata

  • Authors:

  • Zorana Jančić;Jelena Ignjatović;Miroslav irić

  • Affiliations:

  • University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia;University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia;University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

For a given weighted finite automaton over a strong bimonoid we construct its reduced Nerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics. We show that the reduced Nerode automaton is even smaller than the Nerode automaton, which was previously used in determinization related to this semantics. We determine necessary and sufficient conditions under which the reduced Nerode automaton is finite and provide an efficient algorithm which computes the reduced Nerode automaton whenever it is finite. In determinization of weighted finite automata over semirings and fuzzy finite automata over lattice-ordered monoids this algorithm gives smaller crisp-deterministic automata than any other known determinization algorithm.