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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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Cited by 7 (6 self)
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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
General quantitative specification theories with modalities
 Juhani Karhumäki, Arto Lepistö, and Michail Prilutskii, editors, CSR, volume 7353 of LNCS
, 2012
"... Abstract. This paper proposes a new theory of quantitative specifications. It generalizes the notions of stepwise refinement and compositional design operations from the Boolean to an arbitrary quantitative setting. It is shown that this general approach permits to recast many existing problems wh ..."
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Cited by 5 (4 self)
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Abstract. This paper proposes a new theory of quantitative specifications. It generalizes the notions of stepwise refinement and compositional design operations from the Boolean to an arbitrary quantitative setting. It is shown that this general approach permits to recast many existing problems which arise in system design. 1
LowerBound Constrained Runs in Weighted Timed Automata
"... Abstract—We investigate a number of problems related to infinite runs of weighted timed automata, subject to lowerbound constraints on the accumulated weight. Closing an open problem from [10], we show that the existence of an infinite lowerboundconstrained run is—for us somewhat unexpectedly—unde ..."
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Cited by 4 (1 self)
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Abstract—We investigate a number of problems related to infinite runs of weighted timed automata, subject to lowerbound constraints on the accumulated weight. Closing an open problem from [10], we show that the existence of an infinite lowerboundconstrained run is—for us somewhat unexpectedly—undecidable for weighted timed automata with four or more clocks. This undecidability result assumes a fixed and known initial credit. We show that the related problem of existence of an initial credit for which there exists a feasible run is decidable in PSPACE. We also investigate the variant of these problems where only boundedduration runs are considered, showing that this restriction makes our original problem decidable in NEXPTIME. Finally, we prove that the universal versions of all those problems (i.e, checking that all the considered runs satisfy the lowerbound constraint) are decidable in PSPACE. I.
Optimal Bounds for Multiweighted and Parametrised Energy Games
, 2013
"... Multiweighted energy games are twoplayer multiweighted games that concern the existence of infinite runs subject to a vector of lower and upper bounds on the accumulated weights along the run. We assume an unknown upper bound and calculate the set of vectors of upper bounds that allow an infinite ..."
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Cited by 4 (2 self)
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Multiweighted energy games are twoplayer multiweighted games that concern the existence of infinite runs subject to a vector of lower and upper bounds on the accumulated weights along the run. We assume an unknown upper bound and calculate the set of vectors of upper bounds that allow an infinite run to exist. For both a strict and a weak upper bound we show how to construct this set by employing results from previous works, including an algorithm given by Valk and Jantzen for finding the set of minimal elements of an upward closed set. Additionally, we consider energy games where the weight of some transitions is unknown, and show how to find the set of suitable weights using the same algorithm.
Automated synthesis of reliable and efficient systems through game theory: A case study
 ECCS 2012, Springer Proceedings in Complexity
, 2013
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FIXEDDIMENSIONAL ENERGY GAMES ARE IN PSEUDOPOLYNOMIAL TIME
, 2015
"... We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multidimensional meanpayoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answ ..."
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We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multidimensional meanpayoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudopolynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multidimensional energy games with given initial credit from nonelementary (Brázdil, Jančar, and Kučera, 2010) to 2EXPTIME, thus establishing their 2EXPTIMEcompleteness.
On The Complexity of Counter Reachability
"... Abstract. Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value in a given location. We distinguish three semantics ..."
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Abstract. Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value in a given location. We distinguish three semantics for counter reachability games, according to what happens when a counter value would become negative: the edge is either disabled, or enabled but the counter value becomes zero, or enabled. We consider the problem of deciding the winner in counter reachability games and show that, in most cases, it has the same complexity under all semantics. Surprisingly, under one semantics, the complexity in dimension one depends on whether the objective value is zero or any other integer. 1