Lattice-valued Automata Minimization Algorithm Research, A Few Classes

Lattice-valued automata, as the extension of the classic Mathematic Model—Finite State Automata, constructed by combination of Fuzzy Mathematics, lattice-ordered monoid and Automation, according to changing the state transition function and the input and output functions. The variations of its type and complexities of the models determine the breadth of its application. Giving right classification will not only simplify the theoretical research but also enhance the usability. Ever since the born of finite automata, minimizing of its states has been our concerning topic. Minimizations of lattice-value automates require typical algorithms according to the typical models. Realizations of minimization of specific model make the applications of latticed-value automates more convenient. Many types of lattice-valued automates'minimization, such as Mealy and Mizumoto lattice automata, lattice-valued finite sequential automata and non-deterministic lattice finite automata,etc have already been reachered for long a time, but more and more types of model and algorithms need our concern.More specifically, the main results are shown below:1. Minimization of lattice-valued Moore machine: Firstly, the notion of lattice- valued Moore machine is introduced, then traversing some algebraic properties of this machine and investigate the congruences and homomorphisms of this type machine. The main results indicate that the algebraic properties of lattice-valued Moore machine has close links to the algebraic properties of lattice-ordered monoids which machines take value in. Finally, the minimization algorithm of lattice-valued Moore machines with in finite steps has been shown and the equivalence of the minimal Moore machine with the primal one is proved.2. Minimization of deterministic lattice finite automata: Firstly, the notion of deterministic lattice finite automata are proposed, and the definition of effectual final states and reachable states were shown. Then based on reachable states, we introduce a new equivalence relation which also gives the equivalence class that can be determined by the operation of sets. Finally, an easy-realization constructive description of minimization algorithm of Deterministic Lattice Finite Automata and the example have been shown.3. Minimization of equal input-output lattice automata: Firstly the notion of equal input-output lattice automata and its properties have been given. Then using the notion of complete lattice matrix introduced in chapter 2, beginning with the behavior matrix, we give the definition of statewise equivalence relations and automation equivalence of the equal input-output lattice automata. From the statewise equivalence relations, reducible condition and minimization algorithm of this kind of automata are obtained.We use the methods such as model extension and algorithm popularization combined with theoretical proof and examples demonstration.