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Concurrent Reachability Games
, 2008
"... We consider concurrent twoplayer games with reachability objectives. In such games, at each round, player 1 and player 2 independently and simultaneously choose moves, and the two choices determine the next state of the game. The objective of player 1 is to reach a set of target states; the objecti ..."
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Cited by 67 (22 self)
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We consider concurrent twoplayer games with reachability objectives. In such games, at each round, player 1 and player 2 independently and simultaneously choose moves, and the two choices determine the next state of the game. The objective of player 1 is to reach a set of target states; the objective of player 2 is to prevent this. These are zerosum games, and the reachability objective is one of the most basic objectives: determining the set of states from which player 1 can win the game is a fundamental problem in control theory and system verification. There are three types of winning states, according to the degree of certainty with which player 1 can reach the target. From type1 states, player 1 has a deterministic strategy to always reach the target. From type2 states, player 1 has a randomized strategy to reach the target with probability 1. From type3 states, player 1 has for every real ε> 0 a randomized strategy to reach the target with probability greater than 1 − ε. We show that for finite state spaces, all three sets of winning states can be computed in polynomial time: type1 states in linear time, and type2 and type3 states in quadratic time. The algorithms to compute the three sets of winning states also enable the construction of the winning and spoiling strategies.
Quantitative Solution of OmegaRegular Games
"... We consider twoplayer games played for an infinite number of rounds, with ωregular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor s ..."
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Cited by 60 (18 self)
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We consider twoplayer games played for an infinite number of rounds, with ωregular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game µcalculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games; as a special case, we solve probabilistic turnbased games with ωregular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Büchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to εoptimal, is only guaranteed in games with safety winning conditions.
Distributed Controller Synthesis for Local Specifications
, 2001
"... We consider the problem of synthesizing distributed controllers for reactive systems against local specifications. We show that a larger class of architectures become decidable in comparison to the analogous problem for global specifications. We identify the exact class of architectures for which th ..."
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Cited by 42 (3 self)
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We consider the problem of synthesizing distributed controllers for reactive systems against local specifications. We show that a larger class of architectures become decidable in comparison to the analogous problem for global specifications. We identify the exact class of architectures for which the problem is decidable. Our results also show the decidability of a related realizability problem for local specifications.
Controller synthesis for probabilistic systems
 In Proceedings of IFIP TCS’2004
, 2004
"... Supported by the DFGProject “VERIAM ” and the DFGNWOProject “VOSS”. Supported by the European Research Training Network “Games”. Abstract Controller synthesis addresses the question of how to limit the internal behavior of a given implementation to meet its specification, regardless of the behavi ..."
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Cited by 32 (0 self)
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Supported by the DFGProject “VERIAM ” and the DFGNWOProject “VOSS”. Supported by the European Research Training Network “Games”. Abstract Controller synthesis addresses the question of how to limit the internal behavior of a given implementation to meet its specification, regardless of the behavior enforced by the environment. In this paper, we consider a model with probabilism and nondeterminism where the nondeterministic choices in some states are assumed to be controllable, while the others are under the control of an unpredictable environment. We first consider probabilistic computation tree logic as specification formalism, discuss the role of strategytypes for the controller and show the NPhardness of the controller synthesis problem. The second part of the paper presents a controller synthesis algorithm for automataspecifications which relies on a reduction to the synthesis problem for PCTL with fairness. 1.
Qualitative Determinacy and Decidability of Stochastic Games with Signals
, 2009
"... We consider the standard model of finite twoperson zerosum stochastic games with signals. We are interested in the existence of almostsurely winning or positively winning strategies, under reachability, safety, Büchi or coBüchi winning objectives. We prove two qualitative determinacy results. Fi ..."
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Cited by 27 (5 self)
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We consider the standard model of finite twoperson zerosum stochastic games with signals. We are interested in the existence of almostsurely winning or positively winning strategies, under reachability, safety, Büchi or coBüchi winning objectives. We prove two qualitative determinacy results. First, in a reachability game either player 1 can achieve almostsurely the reachability objective, or player 2 can ensure surely the complementary safety objective, or both players have positively winning strategies. Second, in a Büchi game if player 1 cannot achieve almostsurely the Büchi objective, then player 2 can ensure positively the complementary coBüchi objective. We prove that players only need strategies with finitememory, whose sizes range from no memory at all to doublyexponential number of states, with matching lower bounds. Together with the qualitative determinacy results, we also provide fixpoint algorithms for deciding which player has an almostsurely winning or a positively winning strategy and for computing the finite memory strategy. Complexity ranges from EXPTIME to 2EXPTIME with matching lower bounds, and better complexity can be achieved for some special cases where one of the players is better informed than her opponent.
A.: Automatic verification of competitive stochastic systems
, 2011
"... Abstract. We present automatic verification techniques for the modelling and analysis of probabilistic systems that incorporate competitive behaviour. These systems are modelled as turnbased stochastic multiplayer games, in which the players can either collaborate or compete in order to achieve a p ..."
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Cited by 17 (12 self)
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Abstract. We present automatic verification techniques for the modelling and analysis of probabilistic systems that incorporate competitive behaviour. These systems are modelled as turnbased stochastic multiplayer games, in which the players can either collaborate or compete in order to achieve a particular goal. We define a temporal logic called rPATL for expressing quantitative properties of stochastic multiplayer games. This logic allows us to reason about the collective ability of a set of players to achieve a goal relating to the probability of an event’s occurrence or the expected amount of cost/reward accumulated. We give a model checking algorithm for verifying properties expressed in this logic and implement the techniques in a probabilistic model checker, based on the PRISM tool. We demonstrate the applicability and efficiency of our methods by deploying them to analyse and detect potential weaknesses in a variety of large case studies, including algorithms for energy management and collective decision making for autonomous systems. 1
Strategy improvement for concurrent reachability games
 In Proceedings of the Third Annual Conference on Quantitative Evaluation of Systems. IEEE Computer
, 2006
"... A concurrent reachability game is a twoplayer game played on a graph: at each state, the players simultaneously and independently select moves; the two moves determine jointly a probability distribution over the successor states. The objective for player 1 consists in reaching a set of target state ..."
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Cited by 17 (6 self)
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A concurrent reachability game is a twoplayer game played on a graph: at each state, the players simultaneously and independently select moves; the two moves determine jointly a probability distribution over the successor states. The objective for player 1 consists in reaching a set of target states; the objective for player 2 is to prevent this, so that the game is zerosum. Our contributions are twofold. First, we present a simple proof of the fact that in concurrent reachability games, for all ε>0, memoryless εoptimal strategies exist. A memoryless strategy is independent of the history of plays, and an εoptimal strategy achieves the objective with probability within ε of the value of the game. In contrast to previous proofs of this fact, which rely on the limit behavior of discounted games using advanced Puisieux series analysis, our proof is elementary and combinatorial. Second, we present a strategyimprovement (a.k.a. policyiteration) algorithm for concurrent games with reachability objectives. 1.
The Complexity of Quantitative Concurrent Parity Games
, 2006
"... We consider twoplayer infinite games played on graphs. The games are concurrent, in that at each state the players choose their moves simultaneously and independently, and stochastic, in that the moves determine a probability distribution for the successor state. The value of a game is the maximal ..."
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Cited by 15 (9 self)
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We consider twoplayer infinite games played on graphs. The games are concurrent, in that at each state the players choose their moves simultaneously and independently, and stochastic, in that the moves determine a probability distribution for the successor state. The value of a game is the maximal probability with which a player can guarantee the satisfaction of her objective. We show that the values of concurrent games with ωregular objectives expressed as parity conditions can be decided in NP ∩ coNP. This result substantially improves the best known previous bound of 3EXPTIME. It also shows that the full class of concurrent parity games is no harder than the special case of turnbased stochastic reachability games, for which NP ∩ coNP is the best known bound. While the previous, more restricted NP ∩ coNP results for graph games relied on the existence of particularly simple (pure memoryless) optimal strategies, in concurrent games with parity objectives optimal strategies may not exist, and εoptimal strategies (which achieve the value of the game within a parameter ε> 0) require in general both randomization and infinite memory. Hence our proof must rely on a more detailed analysis of strategies and, in addition to the main result, yields two results that are interesting on their own. First, we show that there exist εoptimal strategies that in the limit coincide with memoryless strategies; this parallels the celebrated result of MertensNeyman for concurrent games with limitaverage objectives. Second, we complete the characterization of the memory requirements for εoptimal strategies for concurrent games with parity conditions, by showing that memoryless strategies suffice for εoptimality for coBüchi conditions.