in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

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 ne...

We consider weighted finite automata over strong bimonoids, where these weight structures can be considered as semirings which might lack distributivity. Then, in general, the well-known run semantics, initial algebra semantics, and transition semantics of an automaton are different. We prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated s...

A cover automaton of a finite language L is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. An algorithm for constructing a minimal cover automaton of a finite language L is given in a recent paper. This paper goes a step further by proposing a procedure for constructing all minimal cover automata of a given finite language L. The conc...

In this paper, we show that for any BL-general L-fuzzy automaton (BL-GLFA) there exists a complete deterministic accessible reduced BL-general L-fuzzy automaton that recognizing the behavior of the BL-GLFA. Also, we prove that for any finite realization β, there exists a minimal complete deterministic BL-GLFA recognizing β. We prove any complete deterministic accessible reduced BL-GLFA is a min...