Good-for-games $ω$-Pushdown Automata

Abstract

We introduce good-for-games ω-pushdown automata (ω-GFG-PDA). These are automata whose nondeterminism can be resolved based on the run constructed thus far. Good-forgameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results show that ω-GFG-PDA are more expressive than deterministic ω-pushdown automata and that solving infinite games with winning conditions specified by ω-GFG-PDA is EXPTIME-complete, i.e., we have identified a new class of ω-contextfree winning conditions for which solving games is decidable. This means in particular that the universality problem is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by ω-GFG-PDA and decidability of good-for-gameness of ω-pushdown automata and languages.