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Model-checking branching-time properties of probabilistic automata and probabilistic one-counter automata (1502.07549v2)
Published 26 Feb 2015 in cs.LO, cs.FL, and math.LO
Abstract: This paper studies the problem of model-checking of probabilistic automaton and probabilistic one-counter automata against probabilistic branching-time temporal logics (PCTL and PCTL$*$). We show that it is undecidable for these problems. We first show, by reducing to emptiness problem of probabilistic automata, that the model-checking of probabilistic finite automata against branching-time temporal logics are undecidable. And then, for each probabilistic automata, by constructing a probabilistic one-counter automaton with the same behavior as questioned probabilistic automata the undecidability of model-checking problems against branching-time temporal logics are derived, herein.