Abstract:

On the basis of the theory of weighted finite automata,we prove the computing equivalence between two weighted finite automatas under the strong homomorphism of weighted finite automatas, and obtain the quotient weighted automata by establishing the equivalence relation on the states of weighted finite automata.Based on the equivalence relation,the equivalence between weighted finite automata and its quotient automata is also proved.Specifically,the concepts such as commutability,separateness,(strong) connectedness properties and layers of weighted finite automata are introduced,and their relations in two different weighted finite automata are discussed under the homomorphism or strong homomorphism.

Key words: formal power series;weighted finite automata;homomorphism;strong connectedness