An improved algorithm for determinization of weighted and fuzzy automata

For a givenweighted finite automaton over a strong bimonoid we construct its reducedNerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics.We show that the reducedNerode automaton is even smaller than theNerode 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 reducedNerode automaton if it is finite. In determinization ofweighted finite automata over semirings and fuzzy finite automata over lattice-ordered monoids this algorithm gives smaller crispdeterministic automata than any other known determinization algorithm.