Good-for-games $ω$-Pushdown Automata - Lehtinen, Karoliina; Zimmermann, Martin (Logical methods in computer science, 2023)
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 $ω$- pushdown 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. This is a corrected version of the paper arXiv:2001.04392v6 published originally on January 7, 2022.