Accelerating Markov Chain Model Checking: Good-for-Games Meets Unambiguous Automata

Yong Li, Soumyajit Paul, Sven Schewe, Qiyi Tang

Abstract: Good-for-Games (GfG) automata require that their nondeterminism can be resolved on-the-fly, while unambiguous automata guarantee that no word has more than one accepting run. These two mutually exclusive ways of restricted nondeterminism play their roles independently in Markov chain model checking (MCMC) for almost a decade but synthesising them seems hopeless: an automaton that is both GfG and unambiguous is essentially deterministic. This work breaks this perception by combining the strengths of unambiguity with the GfG co-Büchi minimisation recently proposed by Abu Radi and Kupferman. More precisely, this combination allows us to turn unambiguous automata to certain types of probabilistic automata that can be used for MCMC. The resulting automata can be exponentially smaller, and we have provided a family of automata exemplifying this state space reduction, which translates into a significant acceleration of MCMC.