On the Complexity of Model-Checking Branching and Alternating-Time Temporal Logics in One-Counter Systems

Vester, Steen

doi:10.1007/978-3-319-24953-7_27

Cited by 5 publications

(4 citation statements)

References 37 publications

(57 reference statements)

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“…The other quantitative extensions we know of concern ATL/ATL , and most of the results are actually adaptations of similar (decidability) results for the corresponding extensions of CTL and CTL ; this includes probabilistic ATL [32], timed ATL [25,52], multi-valued ATL [53], and weighted versions of ATL [27,62,81]. Finally, some works have considered non-quantitative ATL with quantitative constraints on the set of allowed strategies [1,38], proving the decidability of the model-checking problem.…”

Section: Related Workmentioning

confidence: 87%

Reasoning about Quality and Fuzziness of Strategic Behaviors

Bouyer

Kupferman

Markey

et al. 2023

ACM Trans. Comput. Logic

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Temporal logics are extensively used for the specification of on-going behaviors of computer systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going strategic behaviors in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable the specifier to formalize concepts such as certainty or quality. In the first class, SL ( Strategy Logic ) is one of the most natural and expressive logics describing strategic behaviors. In the second class, a notable logic is \(\mathrm{LTL}[{\mathcal {F}}] \) , which extends LTL with quality operators . In this work we introduce and study \(\mathrm{SL}[{\mathcal {F}}] \) , which enables the specification of quantitative strategic behaviors. The satisfaction value of an \(\mathrm{SL}[{\mathcal {F}}] \) formula is a real value in [0, 1], reflecting “how much” or “how well” the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of \(\mathrm{SL}[{\mathcal {F}}] \) in quantitative reasoning about multi-agent systems, showing how it can express and measure concepts like stability in multi-agent systems, and how it generalizes some fuzzy temporal logics. We also provide a model-checking algorithm for \(\mathrm{SL}[{\mathcal {F}}] \) , based on a quantitative extension of Quantified CTL ⋆ . Our algorithm provides the first decidability result for a quantitative extension of Strategy Logic. In addition, it can be used for synthesizing strategies that maximize the quality of the systems’ behavior.

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Section: Related Workmentioning

confidence: 87%

Reasoning about Quality and Fuzziness of Strategic Behaviors

Bouyer

Kupferman

Markey

et al. 2023

ACM Trans. Comput. Logic

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show abstract

“…The other quantitative extensions we know of concern ATL/ATL * , and most of the results are actually adaptations of similar (decidability) results for the corresponding extensions of CTL and CTL * ; this includes probabilistic ATL [29], timed ATL [46,22], multivalued ATL [47], and weighted versions of ATL [54,24,65]. Finally, some works have considered non-quantitative ATL with quantitative constraints on the set of allowed strategies [1,35], proving decidability of the model-checking problem.…”

Section: Related Workmentioning

confidence: 96%

Reasoning about Quality and Fuzziness of Strategic Behaviours

Bouyer

Kupferman

Markey

et al. 2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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Temporal logics are extensively used for the specification of on-going behaviours of reactive systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going strategic behaviours in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable the specifier to formalise concepts such as certainty or quality. We introduce and study SL[F]-a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviours. The satisfaction value of an SL[F] formula is a real value in [0, 1], reflecting "how much" or "how well" the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of SL[F] in quantitative reasoning about multi-agent systems, by showing how it can express concepts of stability in multi-agent systems, and how it generalises some fuzzy temporal logics. We also provide a model-checking algorithm for our logic, based on a quantitative extension of Quantified CTL ⋆ .

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“…This approach does not work, if the formulae were interpreted on pairs (s, v) ∈ S × N, see e.g. (Vester 2014, Section 4).…”

Section: Given B ∈ N and An Infinite Computationmentioning

confidence: 99%

“…Adding resources to ATL-like logics can be done in many ways, see e.g. (Alechina et al 2009;Bulling and Farwer 2010;Alechina et al 2017;Bulling and Goranko 2022) (see also (Laroussinie, Markey, and Oreiby 2006;Vester 2014)). This is a natural framework in which each action done by some agent either consumes or produces resources.…”

Section: Introductionmentioning

confidence: 99%

How to Manage a Budget with ATL+

Demri

Rönnholm

2023

Proceedings of the Twentieth International Conference on Principles of Knowledge Representation and Reasoning

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We study the alternating-time temporal logic ATL+ enriched with one resource (written ATL+(1)) extending ATL+ with the possibility to manage a budget. We propose a game-theoretic semantics via the introduction of two evaluation games so that the compositional semantics is captured by strategies in the games. We show that the model-checking problem for ATL+(1) is in PSpace and we identify several non-trivial fragments that can be solved in PTime. By-products of our investigations include also a simplified Pspace decision procedure for resource-free ATL+, an effective way to synthesize constraints in a version of ATL+(1) with parameters and a PSpace bound to solve an energy game with one counter whose objectives are LTL formulae of temporal depth one.

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On the Complexity of Model-Checking Branching and Alternating-Time Temporal Logics in One-Counter Systems

Cited by 5 publications

References 37 publications

Reasoning about Quality and Fuzziness of Strategic Behaviors

Reasoning about Quality and Fuzziness of Strategic Behaviors

Reasoning about Quality and Fuzziness of Strategic Behaviours

How to Manage a Budget with ATL+

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