Synchronous Lattice-valued Automata And Synchronous Lattice-valued Finite Automata

Automata theory is the basic of research of algorithm description and analysis, the theory of computation complexity , and computability, etc. It provides a reliable mathematical model of computation theory. Fuzzy automaton also serves a powerful tool as studying and treating natural languages which include fuzziness, and must serve a suitable formal method as soft computing theory based on words.In this dissertation , we mainly study two kinds of automata which take truth values in a general algebraic system-lattice-ordered monoid L as denoted below (I) and (II), respectively.(I) A=(Q,X,Y,δ')(A = (Q,X,Y,M1)),(II) A=(Q,X,Y,δ",σ) (A=(Q,X,Y,M2,O))where Q is a nonempty finite the set of internal states, X is a nonempty finite the set of input symbols, Y is a nonempty finite the set of output symbols, (X|Y) represents the set of all input-output symbols pairs (x\y) of the same length of input symbols and output symbols over X and Y, δ': Q×X×Y×Q → L is a fuzzy transition-output function, denoted as δ'qql(x|y), it is interpreted as the grade membership that the automata (I) will enter state q' and output symbol y with the present state q and the input symbol x, M1 = {M(x|y)|M(x|y) = (mqq'(x|y)), x ∈ X,y ∈Y,q,q' ∈ Q,mgg'(x|y) ∈ L} denotes transition-output matrix for (I); δ" : Q × X× Q → L is a fuzzy transition function for (II), denoted as δ''qq'(x), it is interpreted as the grade membership that the automata (II) will enter state q' with the present state q and the input symbol x, σ : Q×X×Y → L is a, fuzzy output function for (II), denoted as σq(x|y), it is regarded as the grade membership that the automata (II) emits output symbols y at the state q after being equipped with input symbol x, M2 = {M(x)|M(x) = (mqq'(x)),x ∈ X,q,q' ∈ Q,mqq'(x) ∈ L) denotes transition matrix for (II), O = {O(x|y)|O(x|y) = (σg(x|y)),x ∈X,y∈Y,q∈ Q,σq(x|y) ∈ L} denotes output matrix for (II). Since these two kinds of automata have the same...