Logic for ω-pushdown automata

Droste, Manfred; Dziadek, Sven; Kuich, Werner

doi:10.1016/j.ic.2020.104659

Cited by 2 publications

(1 citation statement)

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“…Such characterizations haven been exhibited for contextfree languages of finite [LST94] and infinite words [DDK20] as well as for the class of visibly pushdown languages [AM04]. However, there is, to the best of our knowledge, no characterization of the deterministic contextfree languages, neither for finite nor infinite words.…”

Section: Discussionmentioning

confidence: 91%

Good-for-games $\omega$-Pushdown Automata

Lehtinen¹,

Zimmermann²

2023

Logical Methods 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.

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Section: Discussionmentioning

confidence: 91%