中文摘要：

加权有限自动机是处理不确定环境下的计算的一种通用数学模型．文章对加权有限自动机及其乘积的结构作了进一步的研究．引入了加权变换半群和商变换半群的概念，并依据半环自身的结构，给出了加权有限自动机诱导的商变换半群有限的条件．讨论了加权有限自动机在各种乘积情形下的状态转移函数的性质，并建立了加权有限自动机的乘积（级联积）与其对应的商变换半群之间的关系，为进一步研究加权有限自动机的结构奠定了基础．

英文摘要：

Weighted finite automata are the universal mathematical models pro- cessing of the environment with uncertainty. This paper is the further research on weighted finite automata and the product structure of weighted finite automata. The concepts of weighted transformation semigroups and quotient transformation semi- groups are established. According to the structure of semirings, we give a condition for the induced quotient transformation semigroups being finite for weighted finite automata. We discuss the properties of states transition function of weighed finite automata under different products, and then we establish a relationship betweenweighted sponding structure finite automata under the direct product （cascade product） and quotient transformation semigroups. It is an important step to of weighted finite automata. the corre- study the