Minimizing Running Costs in Consumption Systems

Brázdil, Tomǎš; Klaška, David; Kuăera, Antonín; Novotný, Petr

doi:10.1007/978-3-319-08867-9_30

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…Recent work of Brázdil et al [8] considers the optimization of a payoff under energy constraint. They study mean-payoff in consumption systems, i.e., simplified one-player energy games where all edges consume energy but some states can atomically produce a reload of the energy up to the allowed capacity.…”

Section: Related Workmentioning

confidence: 99%

Average-energy games

et al. 2016

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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. Work partially supported by European project CASSTING (FP7-ICT-601148) and ERC project EQualIS (StG-308087). Mickael Randour is an F.R.S.-FNRS Postdoctoral Researcher.

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Section: Related Workmentioning

confidence: 99%

Average-energy games

et al. 2016

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“…Consumption systems were introduced in [14] in the form of consumption games with multiple resource types. Minimizing mean-payoff in automata with consumption constraints was studied in [16].…”

Section: Models Of Resource-constrained Systems and Limitations Of Currmentioning

confidence: 99%

Qualitative Controller Synthesis for Consumption Markov Decision Processes

Blahoudek

Brázdil

Novotný

et al. 2020

Computer Aided Verification

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Consumption Markov Decision Processes (CMDPs) are probabilistic decision-making models of resource-constrained systems. In a CMDP, the controller possesses a certain amount of a critical resource, such as electric power. Each action of the controller can consume some amount of the resource. Resource replenishment is only possible in special reload states, in which the resource level can be reloaded up to the full capacity of the system. The task of the controller is to prevent resource exhaustion, i.e. ensure that the available amount of the resource stays non-negative, while ensuring an additional linear-time property. We study the complexity of strategy synthesis in consumption MDPs with almost-sure Büchi objectives. We show that the problem can be solved in polynomial time. We implement our algorithm and show that it can efficiently solve CMDPs modelling real-world scenarios.

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“…Some work on other models dealing with energy have been studied, as battery edge systems [4] and consumption games [8]. In the latter games, minimization of running costs have also been investigated [10]. Optimizing the expected mean-payoff in energy MDP's have been studied in [11].…”

Section: Related Workmentioning

confidence: 99%

Energy mean-payoff games

Bruyère,

Hautem,

Randour

et al. 2019

Preprint

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In this paper, we study one-player and two-player energy mean-payoff games. Energy mean-payoff games are games of infinite duration played on a finite graph with edges labeled by 2-dimensional weight vectors. The objective of the first player (the protagonist) is to satisfy an energy objective on the first dimension and a mean-payoff objective on the second dimension. We show that optimal strategies for the first player may require infinite memory while optimal strategies for the second player (the antagonist) do not require memory. In the one-player case (where only the first player has choices), the problem of deciding who is the winner can be solved in polynomial time while for the two-player case we show co-NP membership and we give effective constructions for the infinite-memory optimal strategies of the protagonist. ACM Subject ClassificationSoftware and its engineering → Formal methods; Theory of computation → Logic and verification; Theory of computation → Solution concepts in game theory Keywords and phrases two-player zero-sum games played on graphs, energy and mean-payoff objectives, complexity study and construction of optimal strategies Digital Object Identifier 10.4230/LIPIcs...

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Minimizing Running Costs in Consumption Systems

Cited by 5 publications

References 15 publications

Average-energy games

Average-energy games

Qualitative Controller Synthesis for Consumption Markov Decision Processes

Energy mean-payoff games

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