Determinization of weighted finite automata over strong bimonoids

Determinization of fuzzy automata via factorization of fuzzy states

“…More recently, Ć irić et al [10] consider WFAs over strong bimonoids and study the necessary and sufficient conditions for determinization of this kind of automata. An improved algorithm for determinization of FFAs over strong bimonoids by using the transition sets method [12], is provided by Jančić et al [19].…”

An improved algorithm for determinization of weighted and fuzzy automata☆

“…Not long afterwards Nerode automata were also associated with weighted finite automata over strong bimonoids (cf. [13]). However, there are three different definitions of the behavior of such automata: the run semantics, the initial algebra semantics, and the transition semantics.…”

“…The Nerode automaton A N is equivalent to the original automaton A with respect to the initial algebra semantics, and with respect to the transition and run semantics, crisp-deterministic automata equivalent to A are respectively the Myhill automaton A M and the run automaton A p (cf. [13,20]). Each of these three automata can have strictly less number of states than the other two automata.…”

“…Each of these three automata can have strictly less number of states than the other two automata. In particular, in [13] certain examples were given which demonstrate that finiteness of A N and A M , and definability of A p , are completely independent of each other, i.e., for a wfa A all combinations of finiteness/infiniteness of A N and A M , and definability/undefinability of A p are possible. But, in the case of semirings all three semantics coincide for every weighted finite automaton, and in this case the Nerode automaton always has cardinality smaller than or equal to the cardinalities of the corresponding Myhill automaton and run automaton.…”

“…As usual, we identify the structure (K, +, Á, 0, 1) with its carrier set K. We call K a strong bimonoid if the operation + is commutative and 0 acts as multiplicative zero, i.e., a Á 0 = 0 = 0 Á a for every a 2 K. We say that a strong bimonoid K is right distributive, if it satisfies (a + b) Á c = a Á c + b Á c for every a, b, c 2 K; we call K left distributive, if a Á (b + c) = a Á b + a Á c for every a, b, c 2 K. A semiring is a strong bimonoid which is both left and right distributive. In [13,15] there is a list of examples of strong bimonoids. Here we only remind that every bounded lattice is a strong bimonoid.…”