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The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and complexity theory. In this paper, we develop an abstract setting for studying and solving such games, based on function optimization over certain discrete structures. We introduce new classes of recursively local-global (RLG) and partial recursively local-global (PRLG) functions, and show that strategy evaluation functions for simpledoi:10.1016/j.tcs.2005.07.041 fatcat:u3gsujjxkjflzfu5ndcr6cgqru