Weak Bisimulation for (max/+) Automata and Related Models

In this paper we propose a notion of weak bisimulation for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring. In particular the (max/+), (min/+) or (max/min) dioid are considered. The proposed bisimulation is a natural extension of Milner’s well known weak bisimulation for untimed automata (i. e., weighted automata over the boolean semiring). It is shown that weakly equivalent automata yield identical results with respect to the weights of arbitrarily labelled paths. The basic steps of an algorithm for the computation of the largest weak bisimulation relation for a given weighted automaton is outlined. Furthermore we present composition operations for weighted automata and prove that weak bisimulation is a congruence according to the composition operations presented in this paper.