Averaging in LTL

Bouyer, Patricia; Markey, Nicolas; Matteplackel, Raj Mohan

doi:10.1007/978-3-662-44584-6_19

Cited by 34 publications

(38 citation statements)

References 27 publications

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“…Baier and others have focused on a variant of SL in a stochastic setting [10]; model checking was proven decidable for memoryless strategies, and undecidable in the general case. A quantitative version of SL with Boolean goals over one-counter games has been considered in [16]; only a periodicity property was proven, and no model-checking algorithm is known in that setting as well. Finally, Graded SL [8] extends SL by quantifying on the number of strategies witnessing a given strategy quantifier, and is decidable.…”

Section: Related Workmentioning

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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Section: Related Workmentioning

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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“…Weighted LTL has been investigated over De Morgan algebras [25], arbitrary bounded lattices [15], idempotent zero-divisor free totally commutative complete semirings [28,30], with averaging modalities [5], with discounting over the interval [0, 1] [1,2], and with discounting over the max-plus semiring [28,29]. Recently, a type of weighted LTL has been applied to robotics [26].…”

Section: Corollary 29 Let K Be a Totally Commutative Complete Semirinmentioning

confidence: 99%

“…In [15] the authors proved several characterizations of LTLdefinable and LTL-ω-definable series over arbitrary bounded lattices. Recently, a weighted LTL with averaging modalities was studied in [5], and a weighted LTL over idempotent and zero-divisor free semirings satisfying completeness axioms was investigated in [28,30]. In [1,2] the authors considered a discounted LTL with values in [0, 1] and in [28,29] in the max-plus semiring.…”

Section: Introductionmentioning

confidence: 99%

Weighted Linear Dynamic Logic

Droste¹,

Rahonis²

2016

Electron. Proc. Theor. Comput. Sci.

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We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental Schützenberger theorem. Surprisingly, the equivalence does not require any restriction to our weighted LDL. Our results hold over arbitrary (resp. totally complete) semirings for finite (resp. infinite) words. As a consequence, the equivalence problem for weighted LDL formulas over fields is decidable in doubly exponential time. In contrast to classical logics, we show that our weighted LDL is expressively incomparable to weighted LTL for finite words. We determine a fragment of the weighted LTL such that series over finite and infinite words definable by LTL formulas in this fragment are definable also by weighted LDL formulas.

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“…A version of nested weighted automata over finite words has been studied in [7], and nested weighted automata over infinite words have been studied in [23]. Several quantitative logics have also been studied, such as [6,8,1]. While a substantial work has been done for quantitative automata and logics, quite surprisingly none of the above works consider the automata (or the logic) under probabilistic semantics that we consider in this work.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Automata under Probabilistic Semantics

Chatterjee

Henzinger

Otop³

2016

Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science

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Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider.

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Averaging in LTL

Cited by 34 publications

References 27 publications

Reasoning about Quality and Fuzziness of Strategic Behaviours

Reasoning about Quality and Fuzziness of Strategic Behaviours

Weighted Linear Dynamic Logic

Quantitative Automata under Probabilistic Semantics

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