Good-for-games ω-Pushdown Automata

We introduce good-for-games ω-pushdown automata (ω-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata.

Our main results are that ω-GFG-PDA are more expressive than deterministic ωpushdown automata and that solving infinite games with winning conditions specified by ω-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of ω-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for ω-GFG-PDA 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. Finally, we compare ω-GFG-PDA to ω-visibly PDA, study the resources necessary to resolve the nondeterminism in ω-GFG-PDA, and prove that the parity index hierarchy for ω-GFG-PDA is infinite.