The realization problems related to weighted transducers over strong bimonoids

In this paper, the concepts of weighted transducers over strong bimonoids and their input-output-functions are introduced. Further more, the input-functions and output-functions induced by the input-output-functions of weighted transducers over strong bimonoids are given. It is the most important that the input-functions and output-functions of weighted transducers over strong bimonoids can be realized by weighted finite automata over strong bimonoids, and the realization does not depend on the distributive law, which also embodies the applications of weighted finite automata over strong bimonoids.