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A pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condi- tion in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a push- down automaton. An EXPTIME procedure for finding a winner in a pushdown game is presented. The procedure is then used to solve the model-checking problem for the pushdown processes and the proposi- tional µ-calculus. The problem is shown to be DEXPTIME-complete.

Pushdown processes: Games and model checking