Two Types Of Automata Product

Product is one of the basic operations of automata theory, which plays a prominent role both in theory and application. The algebraic methods is used in the theory of product of fuzzy automata to study the transfer (output) structure of fuzzy finite state automata, that is, to study the characteristics of fuzzy state transition (output) function. This paper costructs the new product of fuzzy finite state automata—Kronecker productis, which discusses the properties of transfer function.Automata consists of two main structures, the transfer structure and output structure.The transfer structure is internal part of automata while the output structure is external part.The output structure is depend on the transfer structure while the transfer structure is independ on the output structure. Hence the transfer structure can be studied separately. This thesis is studies by fuzzy finite state automata with the output function—some algebraic properties of fuzzy finite state automata, because there are research results of fuzzy finite state automata with non- output function.More specifically, the main results are shown below:1. In the framework of matrix theory, the concepts of transition matrix, transformation matrix semigroup, matrix direct sum, matrix sum, as well as covering for fuzzy finite state machines are introduced. The definitions of new products of fuzzy finite state machines are given by application of Kronecker product. Furthermore, the covering properties of matrix direct sum and matrix sum , the distribution law kronecker product and matrix direct sum, kronecker product and matrix sum are proved. Finally, Kronecker product and matrix sum of Mealy-type fuzzy finite state machines are associative. However, it can easily be shown that matrix direct sum of Mealy-type fuzzy finite state machines was not associative.2.The relationships of covering among product machines for Mealy-type fuzzy finite-state machine are studied in detail. The concept of covering is generalized. This new concept is reasonable and valid which is examined by properties. The more covering relationships have been established in the product machines than before. Specially, the covering relationships among the direct product, cascade product, wreath product are proved. Some transitive properties of covering relationships are obtained in the product machines.