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Automata theory is the study of discrete digital system function, structure and the relationship between mathematical theory which aims to study automata analysis and synthesis problems of finite tree automata theory is a branch of automata theory, with the digital computer , digital communications and automation science and technology and the emergence and development of finite tree automata theory in theory and practice is playing an increasingly important role. finite tree automata main contents and general parallel automata theory, it on the one hand to promote the results of the automatic machine has, it also made a number of new problems, enrich the content of automata theory this paper algebra as a tool for partial finite tree automata and fuzzy algebraic structure of tree automata nature to study and discuss the limited recognition fuzzy tree automata some characteristics of language paper is divided into five parts, the first of four parts in each section in a chapter, the last part of the conclusion first chapter is the introduction, this section briefly describes the the application of finite automata, elaborated ideas and the main content of this paper, and the finite tree automata basic concepts and notation introduced second chapter discusses partial finite tree automata homomorphism, congruence, quotient between relationship, the main results: Theorem 2.2.1 Let Α = (U, Χ, α, A '), Β = (V, Χ, β, B') are two partial finite tree automaton, U = (A, Σ), V = (B, Σ), φ Β is Α to surjective homomorphism, ≡ S of Β on the congruence relation, relationship defined A ≡ R : a 1 ≡ R a 2 iff φ (a 1 ) ≡ S φ (a 2 ), a 1 , a 2 ∈ A, then ≡ R congruence on the Α relationship and Α / ≡ R and Β / ≡ S isomorphic. Theorem 2.2.2 Let Α = (U, Χ, α, A ' ) for the partial finite tree automata, U = (A, Σ), if ≡ R , ≡ S are Α relationship and on the congruence ≡ R (?) ≡ S , then Α / ≡ S is Α / ≡ R full homomorphic image. Theorem 2.2. 3 Let Α = (U, Χ, α, A '), Β = (V, Χ, β, B') are two partial finite tree automaton, U = (A, Σ), V = (B, Σ ), f is Α to Β surjective homomorphism, ≡ is defined Α Proposition 2.2.1 on a congruence relation Suppose g is Α to Α / ≡ natural homomorphism, then there exists an isomorphism φ : A / ≡ → B, so that the lower figure Exchange: Chapter fuzzy automata congruence with the state and the nature of algebraic structures such as certain conclusions to fuzzy tree automata main results are: Theorem 3.1 Let Α = ( A, Σ, δ, β) is L on fuzzy tree automata and if Α ≡ is a congruence relation on, then Α and Α / ≡ homomorphism. Theorem 3.2 fuzzy tree automata collection of all congruences made a complete lattice fourth chapter discusses two finite fuzzy tree automata with state and identify relationships between sets, proved a fuzzy tree automata finite number of states there is little fuzzy quotient finite tree automata with equivalence has discussed the finite fuzzy tree automata and finite tree automata recognize the relationship between language and limited fuzzy tree automata language identified some characteristics of the main results: Theorem 4.1 Let Α = (A, Σ, δ Α , β Α ), Β = (B, Σ, δ Β , β Β ) L-fuzzy tree on finite automata, if Α and Β homomorphism, then Α and Β Equivalence Theorem 4.2 pairs of arbitrary finite fuzzy tree automata Α, its suppliers exist fuzzy tree automata Α / ≡, making Α / ≡ minimal number of states and with Α Equivalence Theorem 4.3 Let (L 1 , ∧, ∨), (L 2 , ∧, ∨) is two lattice, f: L 1 → L 2 is a lattice homomorphism, expand f is f: L 1 T < sub> Σ L 2 T Σ , such that for μ ∈ L 1 T Σ , t ∈ T Σ , with f (μ) (t) = f (μ (t)). If μ ∈ L 1 T Σ to identify fuzzy sets, then f (μ) ∈ L 2 T < sub> Σ is identifiable. Theorem 4.4 Let L be a complete distributive lattice, μ ∈ L T Σ for top stitching compatible fuzzy set, μ (T Σ ) is a finite set, then for any a ∈ L, μ a is recognizable tree languages. Finally some concluding remarks, this paper summarizes the main work and describes future work.
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