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Synthesis for multiobjective stochastic games: An application to autonomous urban driving
 In QEST’13, volume 8054 of LNCS
"... Abstract. We study strategy synthesis for stochastic twoplayer games with multiple objectives expressed as a conjunction of LTL and expected total reward goals. For stopping games, the strategies are constructed from the Pareto frontiers that we compute via value iteration. Since, in general, infin ..."
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Abstract. We study strategy synthesis for stochastic twoplayer games with multiple objectives expressed as a conjunction of LTL and expected total reward goals. For stopping games, the strategies are constructed from the Pareto frontiers that we compute via value iteration. Since, in general, infinite memory is required for deterministic winning strategies in such games, our construction takes advantage of randomised memory updates in order to provide compact strategies. We implement our methods in PRISMgames, a model checker for stochastic multiplayer games, and present a case study motivated by the DARPA Urban Challenge, illustrating how our methods can be used to synthesise strategies for highlevel control of autonomous vehicles. 1
On stochastic games with multiple objectives
 IN MFCS’13, VOLUME 8087 OF LNCS
, 2013
"... We study twoplayer stochastic games, where the goal of one player is to satisfy a formula given as a positive boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and verification of open sy ..."
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Cited by 5 (5 self)
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We study twoplayer stochastic games, where the goal of one player is to satisfy a formula given as a positive boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and verification of open systems with stochastic behaviour. We show that finding a winning strategy is PSPACEhard in general and undecidable for deterministic strategies. We also prove that optimal strategies, if they exists, may require infinite memory and randomisation. However, when restricted to disjunctions of objectives only, memoryless deterministic strategies suffice, and the problem of deciding whether a winning strategy exists is NPcomplete. We also present algorithms to approximate the Pareto sets of achievable objectives for the class of stopping games.
Looking at MeanPayoff and TotalPayoff through Windows
, 2013
"... We consider twoplayer games played on weighted directed graphs with meanpayoff and totalpayoff objectives, two classical quantitative objectives. While for singledimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multidimensional meanp ..."
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We consider twoplayer games played on weighted directed graphs with meanpayoff and totalpayoff objectives, two classical quantitative objectives. While for singledimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multidimensional meanpayoff games that are known to be coNPcomplete, multidimensional totalpayoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving meanpayoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIMEcomplete, and (ii) there is no primitiverecursive algorithm to decide the existence of a bounded window.
A Framework for Automated Competitive Analysis of Online Scheduling of FirmDeadline Tasks
"... Abstract—We present a flexible framework for the automated competitive analysis of online scheduling algorithms for firmdeadline realtime tasks based on multiobjective graphs: Given a taskset and an online scheduling algorithm specified as a labeled transition system, along with some optional s ..."
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Abstract—We present a flexible framework for the automated competitive analysis of online scheduling algorithms for firmdeadline realtime tasks based on multiobjective graphs: Given a taskset and an online scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limitaverage constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. a clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several online algorithms, including Dover, that have been proposed in the past, for various tasksets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are tasksets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application. I.
Limit Your Consumption! Finding Bounds in Averageenergy Games?
"... Abstract. Energy games are infinite twoplayer games played in weighted arenas with quantitative objectives that restrict the consumption of a resource modeled by the weights, e.g., a battery that is charged and drained. Typically, upper and/or lower bounds on the battery capacity are part of the p ..."
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Abstract. Energy games are infinite twoplayer games played in weighted arenas with quantitative objectives that restrict the consumption of a resource modeled by the weights, e.g., a battery that is charged and drained. Typically, upper and/or lower bounds on the battery capacity are part of the problem description. In this work, we consider the problem of determining upper bounds on the average accumulated energy or on the capacity while satisfying a given lower bound, i.e., we do not determine whether a given bound is sufficient to meet the specification, but if there exists a bound that is sufficient to meet it. In the classical setting with positive and negative weights, we show that the problem of determining the existence of a sufficient bound on the longrun average accumulated energy can be solved in doublyexponential time. Then, we consider recharge games: here, all weights are negative, but there are recharge edges that recharge the energy to some fixed capacity. We show that bounding the longrun average energy in such games is complete for exponential time. Then, we consider the existential version of the problem, which turns out to be solvable in polynomial time: here, we ask whether there is a recharge capacity that allows the system player to win the game. We conclude by studying tradeoffs between the memory needed to implement strategies and the bounds they realize. We give an example showing that memory can be traded for bounds and vice versa. Also, we show that increasing the capacity allows to lower the average accumulated energy. 1