Good-for-games ω-Pushdown Automata

Lehtinen, Karoliina; Zimmermann, Martín

doi:10.1145/3373718.3394737

Cited by 9 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, let us remark that GFGness of PDA and context-free languages is undecidable. These problems were shown to be undecidable for ω-GFG-PDA and ω-GFG-CFL by reductions from the inclusion and universality problem for PDA on finite words [25]. Similar proofs also show that these problems are undecidable over PDA on finite words.…”

Section: Good-for-games Pushdown Automatamentioning

confidence: 71%

“…This makes them appealing for applications such as the synthesis of reactive systems, which can be modelled as a game between an antagonistic environment and the system. Solving games is undecidable for PDA in general [12], both over finite and infinite words, while for ω-GFG-PDA, it is ExpTime-complete [25]. As a corollary, universality is also decidable for ω-GFG-PDA, while it is undecidable for PDA, both over finite and infinite words [19].…”

Section: Games and Universalitymentioning

confidence: 99%

“…While the one-token game does not characterise the GFGness of Büchi automata, here we show that it suffices for VPA. The matching lower bound follows from a reduction from the inclusion problem for VPA, which is ExpTime-hard [2], to GFGness (see [25] for details of the reduction in the context of ω-GFG-PDA).…”

Section: Good-for-games Visibly Pushdown Automatamentioning

confidence: 99%

“…Nevertheless, we prove that GFG-PDA are more expressive than DPDA, yielding the first class of automata on finite words where GFG nondeterminism adds expressiveness. The language witnessing the separation is remarkably simple, in contrast to the relatively subtle argument for the infinitary result [25]: the language {a i $a j $b k $ | k max(i, j)} is recognised by a GFG-PDA but not by a DPDA. This yields a new class of languages, those recognised by GFG-PDA over finite words, for which universality and solving games are decidable.…”

Section: Introductionmentioning

confidence: 96%

“…Recently, pushdown automata on infinite words with GFG nondeterminism (ω-GFG-PDA) were shown to be strictly more expressive than ω-DPDA, while universality and solving games for ω-GFG-PDA are not harder than for ω-DPDA [25]. Thus, GFG nondeterminism adds expressiveness without increasing the complexity of these problems, i.e.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

Guha¹,

Jecker²,

Lehtinen³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We also study GFGness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show GFGness to be ExpTimecomplete. GFG-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state resolvers are determinisable.

show abstract

Section: Good-for-games Pushdown Automatamentioning

confidence: 71%

Section: Games and Universalitymentioning

confidence: 99%

Section: Good-for-games Visibly Pushdown Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

Guha¹,

Jecker²,

Lehtinen³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

On (I/O)-Aware Good-For-Games Automata

Faran

Kupferman

2020

Automated Technology for Verification and Analysis

View full text Add to dashboard Cite

Token Games and History-Deterministic Quantitative Automata

Boker

Lehtinen

2022

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

A nondeterministic automaton is history-deterministic if its nondeterminism can be resolved by only considering the prefix of the word read so far. Due to their good compositional properties, history-deterministic automata are useful in solving games and synthesis problems. Deciding whether a given nondeterministic automaton is history-deterministic (the problem) is generally a difficult task, which might involve an exponential procedure, or even be undecidable, for example for pushdown automata. Token games provide a PTime solution to the problem of Büchi and coBüchi automata, and it is conjectured that 2-token games characterise for all $$\omega $$ ω -regular automata. We extend token games to the quantitative setting and analyze their potential to help deciding for quantitative automata. In particular, we show that 1-token games characterise for all quantitative (and Boolean) automata on finite words, as well as discounted-sum ($${\mathsf {DSum}}$$ DSum ) automata on infinite words, and that 2-token games characterise of $${\mathsf {LimInf}}$$ LimInf and $${\mathsf {LimSup}}$$ LimSup automata. Using these characterisations, we provide solutions to the problem of $${\mathsf {Inf}}$$ Inf and $${\mathsf {Sup}}$$ Sup automata on finite words in PTime, for $${\mathsf {DSum}}$$ DSum automata on finite and infinite words in NP$$\cap $$ ∩ co-NP, for $${\mathsf {LimSup}}$$ LimSup automata in quasipolynomial time, and for $${\mathsf {LimInf}}$$ LimInf automata in exponential time, where the latter two are only polynomial for automata with a logarithmic number of weights.

show abstract

Good-for-games ω-Pushdown Automata

Cited by 9 publications

References 11 publications

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

On (I/O)-Aware Good-For-Games Automata

Token Games and History-Deterministic Quantitative Automata

Contact Info

Product

Resources

About