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Generalized meanpayoff and energy games
 CoRR
"... In meanpayoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized meanpayoff and energy games replace in ..."
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In meanpayoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized meanpayoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resourcebounded processes with multiple resources. We prove the finitememory determinacy of generalized energy games and show the interreducibility of generalized meanpayoff and energy games for finitememory strategies. We also improve the computational complexity for solving both classes of games with finitememory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNPcomplete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NPcomplete. Digital Object Identifier 10.4230/LIPIcs.FSTTCS.2010.505 1
Church synthesis problem for noisy input
 In Proc. of FOSSACS, LNCS 6604
, 2011
"... Abstract. We study two variants of infinite games with imperfect information. In the first variant, in each round player1 may decide to hide his move from player2. This captures situations where the input signal is subject to fluctuations (noises), and every error in the input signal can be detec ..."
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Cited by 9 (3 self)
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Abstract. We study two variants of infinite games with imperfect information. In the first variant, in each round player1 may decide to hide his move from player2. This captures situations where the input signal is subject to fluctuations (noises), and every error in the input signal can be detected by the controller. In the second variant, all of player1 moves are visible to player2; however, after the game ends, player1 may change some of his moves. This captures situations where the input signal is subject to fluctuations; however, the controller cannot detect errors in the input signal. We consider several cases, according to the amount of errors allowed in the input signal: a fixed number of errors, finitely many errors and the case where the rate of errors is bounded by a threshold. For each of these cases we consider games with regular and meanpayoff winning conditions. We investigate the decidability of these games. There is a natural reduction for some of these games to (perfect information) multidimensional meanpayoff games recently considered in [6]. However, the decidability of the winner of multidimensional meanpayoff games was stated as an open question. We prove its decidability and provide tight complexity bounds. 1
A.: Emptiness and Universality Problems in Timed Automata with Positive Frequency
 ICALP 2011, Part II. LNCS
, 2011
"... Abstract. The languages of infinite timed words accepted by timed automata are traditionally defined using Büchilike conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we pro ..."
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Abstract. The languages of infinite timed words accepted by timed automata are traditionally defined using Büchilike conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we propose a natural quantitative semantics for timed automata based on the socalled frequency, which measures the proportion of time spent in the accepting locations. We study various properties of timed languages accepted with positive frequency, and in particular the emptiness and universality problems. 1
Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs
"... We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the meanpayoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative pr ..."
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We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the meanpayoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is wellknown that the controlflow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the meanpayoff value within a multiplicative factor of in time O(n · log(n/)) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n · log(a · b)) = O(n · log(n ·W)), when the output is a b, as compared to the previously best known algorithm with running time O(n2 · log(n ·W)). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n2 ·m) time and the associated decision problem can be solved inO(n ·m) time, improving the previous known O(n3 · m · log(n · W)) and O(n2 · m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n · logn) time, improving the previous known O(n4 · log(n ·W)) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
Finitememory strategy synthesis for robust multidimensional meanpayoff objectives
 In CSLLICS
, 2014
"... ar ..."
Emptiness and Universality Problems in Timed Automata with Positive Frequency
, 2011
"... The languages of infinite timed words accepted by timed automata are traditionally defined using Büchilike conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we propose a natur ..."
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Cited by 1 (0 self)
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The languages of infinite timed words accepted by timed automata are traditionally defined using Büchilike conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we propose a natural quantitative semantics for timed automata based on the socalled frequency, which measures the proportion of time spent in the accepting locations. We study various properties of timed languages accepted with positive frequency, and in particular the emptiness and universality problems.