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Meanpayoff parity games
 PROC. OF LICS, IEEE COMPUTER SOCIETY
"... Energy parity games are infinite twoplayer turnbased games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own i ..."
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Cited by 64 (12 self)
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Energy parity games are infinite twoplayer turnbased games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resourceconstrained omegaregular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objective. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is polynomially equivalent to the problem of deciding the winner in meanpayoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve meanpayoff parity games.
Energy and meanpayoff games with imperfect information
 In CSL 2010, volume LNCS 6247
, 2010
"... Abstract. We consider twoplayer games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resour ..."
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Abstract. We consider twoplayer games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resource consumption and the objective of the game is to maintain the sum of weights always nonnegative. In a meanpayoff game, the objective is to optimize the limitaverage usage of the resource. We show that the problem of determining if an energy game with imperfect information with fixed initial credit has a winning strategy is decidable, while the question of the existence of some initial credit such that the game has a winning strategy is undecidable. This undecidability result carries over to meanpayoff games with imperfect information. On the positive side, using a simple restriction on the game graph (namely, that the weights are visible), we show that these problems become EXPTIMEcomplete. 1
Energy and meanpayoff parity Markov decision processes
, 2011
"... Abstract. We consider Markov Decision Processes (MDPs) with meanpayoff parity and energy parity objectives. In system design, the parity objective is used to encode ωregular specifications, while the meanpayoff and energy objectives can be used to model quantitative resource constraints. The ener ..."
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Abstract. We consider Markov Decision Processes (MDPs) with meanpayoff parity and energy parity objectives. In system design, the parity objective is used to encode ωregular specifications, while the meanpayoff and energy objectives can be used to model quantitative resource constraints. The energy condition requires that the resource level never drops below 0, and the meanpayoff condition requires that the limitaverage value of the resource consumption is within a threshold. While these two (energy and meanpayoff) classical conditions are equivalent for twoplayer games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almostsure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for meanpayoff parity MDPs, the problem is solvable in polynomial time. 1
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.
A Note on the Approximation of MeanPayoff Games
"... Abstract. We consider the problem of designing approximation schemes for the values of meanpayoff games. It was recently shown that (1) meanpayoff with rational weights scaled on [−1, 1] admit additive fullypolynomial approximation schemes, and (2) meanpayoff games with positive weights admit re ..."
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Abstract. We consider the problem of designing approximation schemes for the values of meanpayoff games. It was recently shown that (1) meanpayoff with rational weights scaled on [−1, 1] admit additive fullypolynomial approximation schemes, and (2) meanpayoff games with positive weights admit relative fullypolynomial approximation schemes. We show that the problem of designing additive/relative approximation schemes for general meanpayoff games (i.e. with no constraint on their edgeweights) is Ptime equivalent to determining their exact solution. 1
A SAT ENCODING FOR SOLVING GAMES WITH ENERGY OBJECTIVES
"... Recently, a reduction from the problem of solving parity games to the satisfiability problem in propositional logic (SAT) have been proposed in [5], motivated by the success of SAT solvers in symbolic verification. With analogous motivations, we show how to exploit the notion of energy progress meas ..."
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Recently, a reduction from the problem of solving parity games to the satisfiability problem in propositional logic (SAT) have been proposed in [5], motivated by the success of SAT solvers in symbolic verification. With analogous motivations, we show how to exploit the notion of energy progress measure to devise a reduction from the problem of energy games to the satisfiability problem for formulas of propositional logic in conjunctive normal form. 1.
Down the Borel Hierarchy: Solving Muller Games via Safety Games I
"... We transform a Muller game with n vertices into a safety game with (n!)3 vertices whose solution allows us to determine the winning regions of the Muller game and to compute a finitestate winning strategy for one player. This yields a novel antichainbased memory structure, a compositional solution ..."
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We transform a Muller game with n vertices into a safety game with (n!)3 vertices whose solution allows us to determine the winning regions of the Muller game and to compute a finitestate winning strategy for one player. This yields a novel antichainbased memory structure, a compositional solution algorithm, and a natural notion of permissive strategies for Muller games. Moreover, we generalize our construction by presenting a new type of game reduction from infinite games to safety games and show its applicability to several other winning conditions.