Quantified CTL: Expressiveness and Complexity

Laroussinie, François; Markey, Nicolas

doi:10.2168/lmcs-10(4:17)2014

Cited by 30 publications

(112 citation statements)

References 52 publications

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“…This is a severe limitation in ATL/ATL * and has been studied under the name of irrevocability of strategies in [1]. Remarkably, this feature can be handled with more sophisticated logics such as Strategy Logics [9,24], ATL with strategy contexts [22], and quantified CTL [21]. However, for such logics, the relative model checking question turns out to be non-elementary.…”

Section: Resultsmentioning

confidence: 99%

On the Complexity of ATL and ATL* Module Checking

Bozzelli¹,

Murano²

2017

Electron. Proc. Theor. Comput. Sci.

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Module checking has been introduced in late 1990s to verify open systems, i.e., systems whose behavior depends on the continuous interaction with the environment. Classically, module checking has been investigated with respect to specifications given as CTL and CTL * formulas. Recently, it has been shown that CTL (resp., CTL * ) module checking offers a distinctly different perspective from the better-known problem of ATL (resp., ATL * ) model checking. In particular, ATL (resp., ATL * ) module checking strictly enhances the expressiveness of both CTL (resp., CTL * ) module checking and ATL (resp. ATL * ) model checking. In this paper, we provide asymptotically optimal bounds on the computational cost of module checking against ATL and ATL * , whose upper bounds are based on an automata-theoretic approach. We show that module-checking for ATL is EXPTIME-complete, which is the same complexity of module checking against CTL. On the other hand, ATL * module checking turns out to be 3EXPTIME-complete, hence exponentially harder than CTL * module checking.

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Section: Resultsmentioning

confidence: 99%

On the Complexity of ATL and ATL* Module Checking

Bozzelli¹,

Murano²

2017

Electron. Proc. Theor. Comput. Sci.

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“…First, we point out that if F = {⊤, ∨, ¬}, then BQCTL ⋆ [F ] evaluated on boolean Kripke structures corresponds to classic QCTL ⋆ [52]. Note also that the quantifier on propositions does not range over arbitrary values in [0, 1].…”

Section: Semanticsmentioning

confidence: 99%

“…Clearly, EQ k CTL ⋆ can be translated in BQCTL ⋆ [F ] with formulas of linear size and nesting depth at most k (alternation is simply coded by placing function ¬ between quantifiers). It is proved in [52] that model checking EQ k CTL ⋆ is (k + 1)-Exptime-hard.…”

Section: Model Checking Bqctl ⋆ [F ]mentioning

confidence: 99%

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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“…It only remains to build a simple deterministic tree automaton A over L ϕ -trees such that L(A) = {t}, and check for emptiness of the alternating tree automaton L(A ∩ A ϕ s ). Because nondeterminisation makes the size of the automaton gain one exponential for each nested quantifier on propositions, the procedure is nonelementary, and hardness is inherited from the model-checking problem for QCTL [16].…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…As a tool to study SL ii we introduce QCTL * ii , an extension to the imperfect-information setting of QCTL * [16], itself an extension of CTL * by second-order quantifiers over atoms. This is a low-level logic that does not mention strategies and into which one can effectively compile instances of SL ii .…”

Section: Introductionmentioning

confidence: 99%

Strategy logic with imperfect information

Berthon

Maubert

Murano

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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We introduce an extension of Strategy logic for the imperfect-information setting, called SL ii , and study its modelchecking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SL ii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems.To establish the decidability result, we introduce and study QCTL * ii , an extension of QCTL (itself an extension of CTL with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL * ii allows us to provide a conceptually neat reduction of SL ii to QCTL * ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL * ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automatatheoretic approach, that it is decidable. The decidability result for SL ii follows since the reduction maps hierarchical instances of SL ii to hierarchical formulas of QCTL * ii .

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Quantified CTL: Expressiveness and Complexity

Cited by 30 publications

References 52 publications

On the Complexity of ATL and ATL* Module Checking

On the Complexity of ATL and ATL* Module Checking

Reasoning about Quality and Fuzziness of Strategic Behaviours

Strategy logic with imperfect information

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