## Karoliina Lehtinen ; Martin Zimmermann - Good-for-games $\omega$-Pushdown Automata

lmcs:6995 - Logical Methods in Computer Science, February 15, 2023, Volume 18, Issue 1 - https://doi.org/10.46298/lmcs-18(1:3)2022
Good-for-games $\omega$-Pushdown Automata

Authors: Karoliina Lehtinen ; Martin Zimmermann

We introduce good-for-games $\omega$-pushdown automata ($\omega$-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 $\omega$-GFG-PDA are more expressive than deterministic $\omega$- pushdown automata and that solving infinite games with winning conditions specified by $\omega$-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for $\omega$-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG- PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages. Finally, we compare $\omega$-GFG-PDA to $\omega$-visibly PDA, study the resources necessary to resolve the nondeterminism in $\omega$-GFG-PDA, and prove that the parity index hierarchy for $\omega$-GFG-PDA is infinite. This is a corrected version of the paper arXiv:2001.04392v6 published originally on January 7, 2022.

Volume: Volume 18, Issue 1
Published on: February 15, 2023
Accepted on: October 4, 2021
Submitted on: December 21, 2020
Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Computer Science and Game Theory,68Q45,F.4.3