Optimal Bounds for Multiweighted and Parametrised Energy Games

Juhl, Line; Larsen, Kim Guldstrand; Raskin, Jean-François

doi:10.1007/978-3-642-39698-4_15

Cited by 28 publications

(26 citation statements)

References 11 publications

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“…Following the publication of [7], Larsen et al adressed a different problem in [32]: they proved that deciding if there exists a threshold t ∈ Q such that P 1 can win a two-player game for objective Energy L (c init := 0) ∩ AvgEnergy(t) can be done in doubly-exponential time. This is indeed equivalent to deciding if there exists an upper-bound U ∈ N such that P 1 can win for the objective Energy LU (U, c init := 0), which is known to be in 2EXPTIME [25]. Unfortunately, this approach does not help in solving Problem 3, where the threshold t ∈ Q for the averageenergy is part of the input: solving two-player AE L games is still an open question.…”

Section: Resultsmentioning

confidence: 99%

Average-energy games

Bouyer

Markey

Randour

et al. 2015

Electron. Proc. Theor. Comput. Sci.

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Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the objective is to optimize the long-run average gain per action, and energy games, where the system has to avoid running out of energy.We study average-energy games, where the goal is to optimize the long-run average of the accumulated energy. We show that this objective arises naturally in several applications, and that it yields interesting connections with previous concepts in the literature. We prove that deciding the winner in such games is in NP ∩ coNP and at least as hard as solving mean-payoff games, and we establish that memoryless strategies suffice to win. We also consider the case where the system has to minimize the average-energy while maintaining the accumulated energy within predefined bounds at all times: this corresponds to operating with a finite-capacity storage for energy. We give results for one-player and two-player games, and establish complexity bounds and memory requirements.

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Section: Resultsmentioning

confidence: 99%

Average-energy games

Bouyer

Markey

Randour

et al. 2015

Electron. Proc. Theor. Comput. Sci.

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“…Even apparently simple problems, such as the task to compute the probability for a weight invariance (wgt > 0) in a Markov chain, turn out to be hard. Our work on ratios in Markovian models is in the line of a current research trend to extend temporal logics, transition systems and game structures with weight functions, see, e.g., [1,11,12,14,16,17,34,39].…”

Section: Discussionmentioning

confidence: 99%

Trade-off analysis meets probabilistic model checking

Baier

Dubslaff

Klüppelholz

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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Probabilistic model checking (PMC) is a well-established and powerful method for the automated quantitative analysis of parallel distributed systems. Classical PMC-approaches focus on computing probabilities and expectations in Markovian models annotated with numerical values for costs and utility, such as energy and performance. Usually, the utility gained and the costs invested are dependent and a trade-off analysis is of utter interest.In this paper, we provide an overview on various kinds of nonstandard multi-objective formalisms that enable to specify and reason about the trade-off between costs and utility. In particular, we present the concepts of quantiles, conditional probabilities and expectations as well as objectives on the ratio between accumulated costs and utility. Such multi-objective properties have drawn very few attention in the context of PMC and hence, there is hardly any tool support in state-of-the-art model checkers. Furthermore, we broaden our results towards combined quantile queries, computing conditional probabilities those conditions are expressed as formulas in probabilistic computation tree logic, and the computation of ratios which can be expected on the long-run.

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“…In the example above, P 0 has a strategy to win for the energy objective with lower bound zero and upper bound six. Energy objectives [3,11,18,19] and their combinations with parity objectives [9,11] have received significant attention in the literature.…”

Section: Introductionmentioning

confidence: 99%

Bounding Average-Energy Games

Bouyer

Hofman

Markey

et al. 2017

Lecture Notes in Computer Science

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Abstract. We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound constraint on the energy level (but no upper bound) remained open; in particular, so far there was no known upper bound on the memory that is required for winning strategies. By reducing average-energy games with lower-bounded energy to infinite-state mean-payoff games and analyzing the density of low-energy configurations, we show an almost tight doubly-exponential upper bound on the necessary memory, and that the winner of average-energy games with lower-bounded energy can be determined in doubly-exponential time. We also prove EXPSPACE-hardness of this problem. Finally, we consider multi-dimensional extensions of all types of average-energy games: without bounds, with only a lower bound, and with both a lower and an upper bound on the energy. We show that the fully-bounded version is the only case to remain decidable in multiple dimensions.

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Optimal Bounds for Multiweighted and Parametrised Energy Games

Cited by 28 publications

References 11 publications

Average-energy games

Average-energy games

Trade-off analysis meets probabilistic model checking

Bounding Average-Energy Games

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