Nondeterministic fuzzy automata

Nondeterministic fuzzy automata

Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property—nondeterminism—in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without -moves and fuzzy languages recognized by them. Furthermor...

Directable Fuzzy and Nondeterministic Automata

We study three notions of directability of fuzzy automata akin to the D1-, D2and D3-directability of nondeterministic automata. Thus an input word w of a fuzzy automaton is D1-directing if a fixed single state is reachable by w from all states, D2-directing if exactly the same states are reachable by w from every state, and D3-directing if there is a state reachable by w from every state. We st...

Canonical Nondeterministic Automata

For each regular language L we describe a family of canonical nondeterministic acceptors (nfas). Their construction follows a uniform recipe: build the minimal dfa for L in a locally finite variety V , and apply an equivalence between the finite V-algebras and a category of finite structured sets and relations. By instantiating this to different varieties we recover three well-studied canonical...

Complementing Unary Nondeterministic Automata

On Monogenic Nondeterministic Automata

A finite automaton is said to be directable if it has an input word, a directing word, which takes it from every state into the same state. For nondeterministic (n.d.) automata, directability can be generalized in several ways, three such notions, D1-, D2-, and D3-directability, are used. In this paper, we consider monogenic n.d. automata, and for each i = 1, 2, 3, we present sharp bounds for t...