Bisimulation relations for weighted automata over valuation monoids

Abstract

In this paper, we firstly give a definition of bisimulation relations for weighted automata over valuation monoids and prove that weighted automata A and B are equivalent with behavior under a bisimulation relation. Then we put forward the notion of surjective functional bisimulation relations and construct the related equivalence relations on A. We also give the properties of these related equivalence relations and define bisimulations relations for A with these properties. Finally, we prove the existence of the greatest bisimulation relation and give the method of constructing the greatest bisimulation relation.