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Meet Your Expectations With Guarantees: Beyond WorstCase Synthesis in Quantitative Games
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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.
Quantitative Games with Interval Objectives
 In FSTTCS 2014
, 2014
"... Traditionally quantitative games such as meanpayoff games and discount sum games have two players – one trying to maximize the payoff, the other trying to minimize it. The associated decision problem, “Can Eve (the maximizer) achieve, for example, a positive payoff? ” can be thought of as one playe ..."
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Traditionally quantitative games such as meanpayoff games and discount sum games have two players – one trying to maximize the payoff, the other trying to minimize it. The associated decision problem, “Can Eve (the maximizer) achieve, for example, a positive payoff? ” can be thought of as one player trying to attain a payoff in the interval (0,∞). In this paper we consider the more general problem of determining if a player can attain a payoff in a finite union of arbitrary intervals for various payoff functions (liminf, meanpayoff, discount sum, total sum). In particular this includes the interesting exactvalue problem, “Can Eve achieve a payoff of exactly (e.g.) 0?” 1
Expectations or Guarantees? I Want It All! A crossroad . . .
, 2014
"... When reasoning about the strategic capabilities of an agent, it is important to consider the nature of its adversaries. In the particular context of controller synthesis for quantitative specifications, the usual problem is to devise a strategy for a reactive system which yields some desired perform ..."
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When reasoning about the strategic capabilities of an agent, it is important to consider the nature of its adversaries. In the particular context of controller synthesis for quantitative specifications, the usual problem is to devise a strategy for a reactive system which yields some desired performance, taking into account the possible impact of the environment of the system. There are at least two ways to look at this environment. In the classical analysis of twoplayer quantitative games, the environment is purely antagonistic and the problem is to provide strict performance guarantees. In Markov decision processes, the environment is seen as purely stochastic: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. In this expository work, we report on recent results [10, 9] introducing the beyond worstcase synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worstcase while providing an higher expected value against a particular stochastic model of the environment given as input. This problem is relevant to produce system controllers that provide nice expected performance in the everyday situation while ensuring a strict (but relaxed) performance threshold even in the event of very bad (while unlikely) circumstances. It has been studied for both the meanpayoff and the shortest path quantitative measures.