Symbolic Algorithms for Infinite-State Games
Class 1 consists of infinite-state structures for which all safety and reachability games can be solved.
Class 2 consists of infinite-state structures for which all ω-regular games can be solved.
Class 3 consists of infinite-state structures for which all nested positive boolean combinations of ω-regular games can be solved.
Class 4 consists of infinite-state structures for which all nested boolean combinations of ω-regular games can be solved.
We give a structural characterization for each class, using equivalence relations on the state spaces of games which range from game versions of trace equivalence to a game version of bisimilarity. We provide infinite-state examples for all four classes of games from control problems for hybrid systems. We conclude by presenting symbolic algorithms for the synthesis of winning strategies (“controller synthesis”) for infinitestate games with arbitrary ω-regular objectives, and prove termination over all class-2 structures. This settles, in particular, the symbolic controller synthesis problem for rectangular hybrid systems.
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