Deciding Simulations on Probabilistic Automata

Probabilistic automata are a central model for concurrent systems exhibiting random phenomena. This paper presents, in a uniform setting, efficient decision algorithms for strong simulation on probabilistic automata, but with subtly different results. The algorithm for strong probabilistic simulation is shown to be of polynomial complexity via a reduction to LP problem, while the algorithm for strong simulation has complexity O(m2n). The former relation allows for convex combinations of transitions in the definition and is thus less discriminative than the latter. As a byproduct, we obtain minimisation algorithms with respect to strong simulation equivalences and - for Markov decision processes - also to strong bisimulation equivalences. When extending these algorithms to the continuous-time setting, we retain same complexities for both strong simulation and strong probabilistic simulations.

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