Winning Strategies & Regions
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This chapter identifies a simple denotational semantics for hybrid games based on their winning regions, i.e., the set of states from which there is a winning strategy that wins the game for all strategies that the opponent might choose. Such a denotational semantics continues the successful trend in this book of understanding all operators in a compositional way. That is, the meaning of a compound hybrid game is a simple function of the meaning of its pieces. For repetitions in hybrid games, such a semantics will turn out to be surprisingly subtle, which will uncover a surprisingly rich complexity in hybrid games that is characteristically different from that of hybrid systems. This is the first indication that hybrid games come with their own unique sets of challenges beyond what hybrid systems already have in store for us.