A maximal entropy stochastic process for a timed automaton (extended version)
Résumé
Several ways of assigning probabilities to runs of timed automata (TA) have been proposed recently. When only the TA is given, a relevant question is to design a probability distribution which represents in the best possible way the runs of the TA. This question does not seem to have been studied yet. We give an answer to it using a maximal entropy approach. We introduce our variant of stochastic model, the stochastic process over runs which permits to simulate random runs of any given length with a linear number of atomic operations. We adapt the notion of Shannon (continuous) entropy to such processes. Our main contribution is an explicit formula defining a process $Y^*$ which maximizes the entropy. This formula is an adaptation of the so-called Shannon-Parry measure to the timed automata setting. The process $Y^*$ has the nice property to be ergodic. As a consequence it has the asymptotic equipartition property and thus the random sampling wrt. $Y^*$ is quasi uniform.
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