Relations Of Some Kinds Of L-valued Finite Automata And Algebraic Properties Of LA-languages

Automa with truth-values in a lattice-ordered monoid are more powerful than other kind of fuzzy automata. Therefore, the study of the relationships of some kinds of automata with truth-values in a lattice-ordered monoid and the study of the algebraic properties of their languages form two very important subjects in fuzzy automata theory.In this thesis, we mainly study the relations of some kinds of L-valued finite automata and the algebraic properties of LA-languages which is based on the references [1,2,3,4].According to the transition function 6 which is deterministic or not, the automata with truth-values in a lattice-ordered monoid A = (Q,Σ,δ,σ₀,σ₁) can be classified into two types, deterministic fuzzy finite automata (DLA for short) and nondeterministic fuzzy finite automaton (LA for short). Moreover, according to whether the initial state σ₀ and the final state σ₁ is deterministic or not, the DLA have three kinds: DLA1, DLA2, DLA3. And the LA have four kinds: LA1, LA2, LA3, LA4. In reference[1], the equivalence of DLA1, DLA2, DLA3 are shown, furthermore it is shown that DLA and LA are not equivalent and the sufficient and necessary condition for the equivalence of DLA, and LA is given. In this paper, the complete relations of LA1, LA2, LA3, LA4 are exploxited: LA1, LA2 and LA3 are equivalent, but LA4 are not equivalent to the former three kinds.The language accepted by an LA is called an LA-language, the language accepted by a DLA is called a DLA-language . In this paper, we also study the algebric properties of LA—languages. It is well known that the following approches to present a languages ï¿¡ are equivalent:(1) L is accepted by some finite automaton;(2) L is accepted by some expresstion;(3) L is accepted by some grammar.In this paper, the algebraic definitions of LA—languages and DLA—languages are given, the equivalence between the algebraic definitions of LA—languages and the...