Decision problems for Turing machines

Finkel, Olivier; Lecomte, Dominique

doi:10.1016/j.ipl.2009.09.002

Cited by 5 publications

(4 citation statements)

References 14 publications

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“…Dynamic logic has been shown to be Π 1 1 -complete in (Meyer et al, 1981); see also (Harel et al, 2000). For further results on ω-languages, see (Finkel & Lecomte, 2009). For the proof of Theorem 6.20, we have made use of their Π 1 2 -completeness result for the problem of deciding whether a non-deterministic Turing machine accepts all ω-words.…”

Section: Related Results In Computer Sciencementioning

confidence: 99%

“…For the proof of Theorem 6.20, we have made use of their Π 1 2 -completeness result for the problem of deciding whether a non-deterministic Turing machine accepts all ω-words. For further results on ω-languages, see (Finkel & Lecomte, 2009). The paper (Harel, 1985) gives a nice exposition of various complexity classes up to Π 1 1 and Σ 1 1 , and illustrates these classes by means of various tiling problems.…”

Section: Related Results In Computer Sciencementioning

confidence: 99%

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On the complexity of stream equality

Endrullis¹,

Hendriks²,

Bakhshi³

et al. 2014

J. Funct. Prog.

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We study the complexity of deciding the equality of streams specified by systems of equations. There are several notions of stream models in the literature, each generating a different semantics of stream equality. We pinpoint the complexity of each of these notions in the arithmetical or analytical hierarchy. Their complexity ranges from low levels of the arithmetical hierarchy such as Π 0 2 for the most relaxed stream models, to levels of the analytical hierarchy such as Π 1 1 and up to subsuming the entire analytical hierarchy for more restrictive but natural stream models. Since all these classes properly include both the semi-decidable and co-semi-decidable classes, it follows that regardless of the stream semantics employed, there is no complete proof system or algorithm for determining equality or inequality of streams. We also discuss several related problems, such as the existence and uniqueness of stream solutions for systems of equations, as well as the equality of such solutions.

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Section: Related Results In Computer Sciencementioning

confidence: 99%

Section: Related Results In Computer Sciencementioning

confidence: 99%

On the complexity of stream equality

Endrullis¹,

Hendriks²,

Bakhshi³

et al. 2014

J. Funct. Prog.

View full text Add to dashboard Cite

show abstract

“…Furthermore, since AAPA can be used to decide inclusion problems for two-tape Büchi automata [Finkel and Lecomte 2009], this result can be strengthened drastically. We refer the interested reader to the extended version for a detailed proof of the strengthened claim.…”

Section: Alternating Asynchronous Parity Automatamentioning

confidence: 99%

Automata and fixpoints for asynchronous hyperproperties

Gutsfeld

Müller-Olm

Ohrem

2021

Proc. ACM Program. Lang.

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Hyperproperties have received increasing attention in the last decade due to their importance e.g. for security analyses. Past approaches have focussed on synchronous analyses, i.e. techniques in which different paths are compared lockstepwise. In this paper, we systematically study asynchronous analyses for hyperproperties by introducing both a novel automata model (Alternating Asynchronous Parity Automata) and the temporal fixpoint calculus H µ , the first fixpoint calculus that can systematically express hyperproperties in an asynchronous manner and at the same time subsumes the existing logic HyperLTL. We show that the expressive power of both models coincides over fixed path assignments. The high expressive power of both models is evidenced by the fact that decision problems of interest are highly undecidable, i.e. not even arithmetical. As a remedy, we propose approximative analyses for both models that also induce natural decidable fragments.

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“…Furthermore, since AAPA can be used to decide inclusion problems for two-tape Büchi automata [Finkel and Lecomte 2009], this result can be strengthened drastically. We refer the interested reader to the appendix for a detailed proof of the strengthened claim.…”

Section: Pmentioning

confidence: 99%

Automata and Fixpoints for Asynchronous Hyperproperties

Gutsfeld¹,

Müller-Olm²,

Ohrem³

2020

Preprint

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Hyperproperties have received increasing attention in the last decade due to their importance e.g. for security analyses. Past approaches have focussed on synchronous analyses, i.e. techniques in which different paths are compared lockstepwise. In this paper, we systematically study asynchronous analyses for hyperproperties by introducing both a novel automata model (Alternating Asynchronous Parity Automata) and the temporal fixpoint calculus , the first fixpoint calculus that can systematically express hyperproperties in an asynchronous manner and at the same time subsumes the existing logic HyperLTL. We show that the expressive power of both models coincides over fixed path assignments. The high expressive power of both models is evidenced by the fact that decision problems of interest are highly undecidable, i.e. not even arithmetical. As a remedy, we propose approximative analyses for both models that also induce natural decidable fragments.

show abstract

Decision problems for Turing machines

Cited by 5 publications

References 14 publications

On the complexity of stream equality

On the complexity of stream equality

Automata and fixpoints for asynchronous hyperproperties

Automata and Fixpoints for Asynchronous Hyperproperties

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