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Emptiness Of Alternating Tree Automata Using Games With Imperfect Information

Abstract : We consider the emptiness problem for alternating tree automata, with two acceptance semantics: classical (all branches are accepted) and qualitative (almost all branches are accepted). For the classical semantics, the usual technique to tackle this problem relies on a Simulation Theorem which constructs an equivalent non-deterministic automaton from the original alternating one, and then checks emptiness by a reduction to a two-player perfect information game. However, for the qualitative semantics, no simulation of alternation by means of non-determinism is known. We give an alternative technique to decide the emptiness problem of alternating tree automata, that does not rely on a Simulation Theorem. Indeed, we directly reduce the emptiness problem to solving an imperfect information two-player parity game. Our new approach can successfully be applied to both semantics, and yields decidability results with optimal complexity; for the qualitative semantics, the key ingredient in the proof is a positionality result for stochastic games played over infinite graphs.
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Nathanaël Fijalkow, Sophie Pinchinat, Olivier Serre. Emptiness Of Alternating Tree Automata Using Games With Imperfect Information. 33rd International Conference on Foundations of Software Technology and Theoretical Computer Science (FST&TCS 2013), 2013, Guwahati, India. pp.13, ⟨10.4230/LIPIcs.FSTTCS.2013.299⟩. ⟨hal-01260682v2⟩



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