On the complexity of linear temporal logic with team semantics

Lück, Martin

doi:10.1016/j.tcs.2020.04.019

Cited by 8 publications

(19 citation statements)

References 9 publications

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“…As we show, variants of our logic can express properties such as synchronicity or fairness for tefs and there is no way in sight to do this in the logic of Baumeister et al [3]. The papers [16,19] study complexity and expressivity properties of LTL with team semantics. In [9], the expressive power of different hyperlogics is compared systematically.…”

Section: Related Workmentioning

confidence: 99%

Temporal Team Semantics Revisited

Gutsfeld¹,

Meier²,

Ohrem³

et al. 2021

Preprint

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In this paper, we study a novel approach to asynchronous hyperproperties by reconsidering the foundations of temporal team semantics. We consider three logics: TeamLTL, TeamCTL and TeamCTL * , which are obtained by adding quantification over so-called time evaluation functions controlling the asynchronous progress of traces. We then relate synchronous TeamLTL to our new logics and show how it can be embedded into them. We show that the model checking problem for ∃TeamCTL with Boolean disjunctions is highly undecidable by encoding recurrent computations of non-deterministic 2-counter machines. Finally, we present a translation of TeamCTL * to Alternating Asynchronous Büchi Automata and obtain decidability results for the path checking problem as well as restricted variants of the model checking and satisfiability problems.

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Section: Related Workmentioning

confidence: 99%

Temporal Team Semantics Revisited

Gutsfeld¹,

Meier²,

Ohrem³

et al. 2021

Preprint

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“…where and 1 A as well as most connectives that have been considered in the literature are shown (e.g., in [14,23]) to be definable in TeamLTL(∼). It is open whether TeamLTL(∼) is expressively complete with respect to properties satisfying some natural invariance, as the corresponding logics in the propositional and modal settings are (see [19,31]).…”

Section: Similarly One Can Show That Every Generalised Atom #mentioning

confidence: 99%

“…However, for TeamLTL with ∨, no meaningful upper bound for the problem was known. The best previous upper bound could be obtained from TeamLTL(∼), for which the problem is highly undecidable [23]. The main source of difficulties comes from the fact that the semantical definition of ∨ does not yield any reasonable compositional brute force algorithm: The verification of (T, i) |= ϕ ∨ ψ with T generated by a finite Kripke structure proceeds by checking that (T 1 , i) |= ϕ and (T 2 , i) |= ψ for some T 1 ∪ T 2 = T , but it can well be that T 1 and T 2 cannot be generated from any finite Kripke structure whatsoever.…”

Section: Hyperqptl + and Decidable Fragments Of Teamltlmentioning

confidence: 99%

“…In [23] Lück established that the model checking problem for TeamLTL(∼) is complete for third-order arithmetics and thus highly undecidable. The proof heavily utilizes the interplay between the Boolean negation ∼ and the disjunction ∨; it was left as an open problem whether some sensible restrictions of the use of the Boolean negation would lead toward discovering decidable logics.…”

Section: Undecidable Extensions Of Teamltlmentioning

confidence: 99%

“…However, most notably, the complexity of model checking under the synchronous semantics was left open. Side stepping the question slightly, it was recently shown that the complexity of satisfiability and model checking of the extension of TeamLTL by the Boolean negation is equivalent to the decision problem of third-order arithmetic [23].…”

Section: Introductionmentioning

confidence: 99%

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Linear-time Temporal Logic with Team Semantics: Expressivity and Complexity

Virtema¹,

Hofmann²,

Finkbeiner³

et al. 2020

Preprint

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We study the expressivity and the model checking problem of linear temporal logic with team semantics (TeamLTL). In contrast to LTL, TeamLTL is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. Logics for hyperproperties have so far been mostly obtained by extending temporal logics like LTL and QPTL with trace quantification, resulting in HyperLTL and HyperQPTL. We study the expressiveness of TeamLTL (and its extensions with downward closed generalised atoms A and connectives such as Boolean disjunction ) in comparison to HyperLTL and HyperQPTL. Thereby, we also obtain a number of model checking results for TeamLTL, a question which is so far an open problem. The two types of logics follow a fundamentally different approach to hyperproperties and are are of incomparable expressiveness. We establish that the universally quantified fragment of HyperLTL subsumes the so-called k-coherent fragment of TeamLTL(A, ). This also implies that the model checking problem is decidable for the fragment. We show decidability of model checking of the so-called left-flat fragment of TeamLTL(A, ) via a translation to a decidable fragment of HyperQPTL. Finally, we show that the model checking problem of TeamLTL with Boolean disjunction and inclusion atom is undecidable.

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Compactness in team semantics

Puljujärvi,

Quadrellaro

2024

Mathematical Logic Qtrly

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We provide two proofs of the compactness theorem for extensions of first‐order logic based on team semantics. First, we build upon Lück's [16] ultraproduct construction for team semantics and prove a suitable version of Łoś' Theorem. Second, we show that by working with suitably saturated models, we can generalize the proof of Kontinen and Yang [13] to sets of formulas with arbitrarily many variables.

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On the complexity of linear temporal logic with team semantics

Cited by 8 publications

References 9 publications

Temporal Team Semantics Revisited

Temporal Team Semantics Revisited

Linear-time Temporal Logic with Team Semantics: Expressivity and Complexity

Compactness in team semantics

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