Decision Algorithms for Probabilistic Bisimulation*

Axiomatizations for Probabilistic Finite-State Behaviors

“…For instance, the notion of weak probabilistic bisimulation defined in [11,6] is decidable for finite-state PA. The reason is that in those works weak transitions are defined in terms of schedulers, and one may get some weak transitions that are not derivable by the (finitary) inference rules used in this paper.…”

“…For instance, consider the transition graph of the above example. The definition of [11,6] allows the underlying probabilistic execution to be infinite as long as that case occurs with probability 0. Hence with that definition one has a weak transition that leads to the distribution θ = {(a, 0 : 1)}.…”

“…these two distributions are enough to characterize all possible weak transitions. By exploiting this property, Cattani and Segala gave a decision algorithm for weak probabilistic bisimulation in [6].…”

“…This approach, which is also known in literature ( [12]), has the advantage of being more formal, and in the case of guarded recursion it is equivalent to the one of [11,6]. In the case of unguarded recursion, however, we feel that it would be more natural to consider also the "limit" weak transitions of [11,6]. The axiomatization of the corresponding notion of observational equivalence is an open problem.…”

“…The last decade has witnessed increasing interest in the area of formal methods for the specification and analysis of probabilistic systems [11,3,15,6]. In [16] van Glabbeek et al classified probabilistic models into reactive, generative and stratified.…”