Good-for-games ω-Pushdown Automata

Lehtinen, Karoliina ORCID: 0000-0003-1171-8790 and Zimmermann, Martin ORCID: 0000-0002-8038-2453
(2020) Good-for-games ω-Pushdown Automata. In: LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science.

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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.

Item Type: Conference or Workshop Item (Unspecified)
Additional Information: Extended version
Uncontrolled Keywords: Good-for-games Automata, Pushdown Automata, Infinite Games, Contextfree languages
Depositing User: Symplectic Admin
Date Deposited: 04 Mar 2020 16:04
Last Modified: 19 Oct 2023 08:47
DOI: 10.1145/3373718.3394737
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