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Probabilistic automata were introduced by Rabin in 1963 as languageacceptors. Two automata are equivalent if and only if they accept each wordwith the same probability. On the other side, in the process algebra community,probabilistic automata were re-proposed by Segala in 1995 which are moregeneral than Rabin's automata. Bisimulations have been proposed for Segala'sautomata to characterize the equivalence between them. So far the two notionsof equivalences and their characteristics have been studied mostlyindependently. In this paper, we consider Segala's automata, and propose anovel notion of distribution-based bisimulation by joining the existingequivalence and bisimilarities. We demonstrate the utility of our definition bystudying distribution-based bisimulation metrics, which gives rise to a robustnotion of equivalence for Rabin's automata. We compare our notions ofbisimulation to some existing distribution-based bisimulations and discusstheir compositionality and relations to trace equivalence. Finally, we show thedecidability and complexity of all relations.

Distribution-based Bisimulation and Bisimulation Metric in Probabilistic Automata