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16
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
Solving parity games on integer vectors
, 2013
"... Abstract. We consider parity games on infinite graphs where configurations are represented by controlstates and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (VASS) and multidimensional energy parity games. We show that the m ..."
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Cited by 5 (0 self)
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Abstract. We consider parity games on infinite graphs where configurations are represented by controlstates and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (VASS) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is interreducible with a subclass of singlesided parity games on VASS where just one player can modify the integer counters and the opponent can only change controlstates. Our main result is that the minimal elements of the upwardclosed winning set of these singlesided parity games on VASS are computable. This implies that the Pareto frontier of the minimal initial credit needed to win multidimensional energy parity games is also computable, solving an open question from the literature. Moreover, our main result implies the decidability of weak simulation preorder/equivalence between finitestate systems and VASS, and the decidability of model checking VASS with a large fragment of the modal µcalculus. 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.
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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Cited by 3 (0 self)
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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.
InfiniteState Energy Games
, 2014
"... Energy games are a wellstudied class of 2player turnbased games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes nonnegative in every component while the oth ..."
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Cited by 3 (0 self)
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Energy games are a wellstudied class of 2player turnbased games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes nonnegative in every component while the other tries to frustrate this. We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of onecounter automata. Our main result is that energy games are decidable in the case where the game graph is induced by a onecounter automaton and the energy is onedimensional. On the other hand, every further generalization is undecidable: Energy games on onecounter automata with a 2dimensional energy are undecidable, and energy games on pushdown automata are undecidable even if the energy is onedimensional. Furthermore, we show that energy games and simulation games are interreducible, and thus we additionally obtain several new (un)decidability results for the problem of checking simulation preorder between pushdown automata and vector addition systems.
Approximate Determinization of Quantitative Automata ∗
"... Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunat ..."
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Cited by 2 (1 self)
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Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunately, important automaton classes, such as sum, discountedsum, and limitaverage automata, cannot be determinized. Yet, the quantitative setting provides the potential of approximate determinization. We define approximate determinization with respect to a distance function, and investigate this potential. We show that sum automata cannot be determinized approximately with respect to any distance function. However, restricting to nonnegative weights allows for approximate determinization with respect to some distance functions. Discountedsum automata allow for approximate determinization, as the influence of a word’s suffix is decaying. However, the naive approach, of unfolding the automaton computations up to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states. We prove matching lower bounds, showing exponential dependency on each of these three parameters. Average and limitaverage automata are shown to prohibit approximate determinization with respect to any distance function, and this is the case even for two weights, 0 and 1.
Automated synthesis of reliable and efficient systems through game theory: A case study
 ECCS 2012, Springer Proceedings in Complexity
, 2013
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Finitememory strategy synthesis for robust multidimensional meanpayoff objectives
 In CSLLICS
, 2014
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