Good-for-games $\omega$-Pushdown Automata
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 determ...
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| Vydáno v: | Logical methods in computer science Ročník 18, Issue 1 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science Association
15.02.2023
Logical Methods in Computer Science e.V |
| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. 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. |
| Author | Lehtinen, Karoliina Zimmermann, Martin |
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| Snippet | We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA).
These are automata whose nondeterminism can be resolved based on the input
processed... We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed... |
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| Title | Good-for-games $\omega$-Pushdown Automata |
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