Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Theoretical Computer Science
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Modalities for model checking (extended abstract): branching time strikes back
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Reasoning about transfinite sequences
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
The complexity of stochastic rabin and streett games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Complexity bounds for regular games
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Controller synthesis and ordinal automata
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Reachability-time games on timed automata
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Games are a classical model in the synthesis of controllers in the open setting. In particular, games of infinite length can represent systems which are not expected to reach a correct state, but rather to handle a continuous stream of events. Yet, even longer sequences of events have to be considered when infinite sequences of events can occur in finite time -- Zeno behaviours. In this paper, we extend two-player games to this setting by considering plays of ordinal length. Our two main results are determinacy of reachability games of length less than ωω on finite arenas, and the PSPACE-completeness of deciding the winner in such a game.