The quest for minimal quotients for probabilistic and Markov automata

One of the prevailing ideas in applied concurrency theory and verification is the concept of automata minimization with respect to strong or weak bisimilarity. The minimal automata can be seen as canonical representations of the behaviour modulo the bisimilarity considered. Together with congruence results wrt. process algebraic operators, this can be exploited to alleviate the notorious state space explosion problem. In this paper, we aim at identifying minimal automata and canonical representations for concurrent probabilistic models. We present minimality and canonicity results for probabilistic and Markov automata modulo strong and weak probabilistic bisimilarity, together with the corresponding minimization algorithms. We also consider weak distribution bisimilarity, originally proposed for Markov automata. For this relation, the quest for minimality does not have a unique answer, since fanout minimality clashes with state and transition minimality. We present an SMT approach to enumerate fanout-minimal models.