The Properties And Minimization Algorithms Of Two Types Of Lattice-valued Finite Automaton

Minimization algorithm of the finite automaton is one of the most important and central issues about the theory of finite automaton. This thesis is concerned with the properties and minimization algorithms of two types of automaton.One type is the Lattice-valued Moore type of finite automaton,the other type is the Lattice-valued finite automaton based on fuzzy-points. This thesis is divided into three chapters. The contents of the thesis are listed as follow:The chapter one,we mainly introduce the theory of the fuzzy set,the properties of lattice-ordered monoid and the congruence and homomorphism on lattice-ordered monoid.The chapter two,we define the Lattice-valued Moore type of finite automaton. Through investigating the properties of the lattice-valued transition function and the lattice-valued output function,we obtain the minimization algorithm on the basis of weak equivalence,and give the instance validation.The chapter three, we advance the Lattice-valued finite automaton based on fuzzy-point(FLM) for the first time. The definition of FLM is given,we mainly study the algebra properties,the ralationship of the FLM and the classical Lattice-valued finite automaton.We define the congruence of the FLM, then discuss the Minimization Algorithm.Finally,we reduce the FLM,get the minimal automaton equivalent to the former.