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46
Temporal specifications with accumulative values
 In LICS
, 2011
"... Abstract—There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitativeoriented specifications ..."
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Abstract—There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitativeoriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the meanpayoff objectives. We investigate the extension of temporal logics with the prefixaccumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the pathaccumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefixaccumulation assertions and extending LTL with pathaccumulation assertions, result in temporal logics whose modelchecking problem is decidable. The extended logics allow to significantly extend the currently known energy and meanpayoff objectives. Moreover, the prefixaccumulation assertions may be refined with “controlledaccumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefixaccumulation assertions permits a decidable modelchecking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable. I.
Strategy synthesis for multidimensional quantitative objectives
 In Proc. of CONCUR, LNCS 7454
, 2012
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The complexity of Nash equilibria in limitaverage games
, 2011
"... Abstract. We study the computational complexity of Nash equilibria in concurrent games with limitaverage objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a Nash equilibrium in pure strategies is decidable, e ..."
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Cited by 12 (3 self)
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Abstract. We study the computational complexity of Nash equilibria in concurrent games with limitaverage objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a Nash equilibrium in pure strategies is decidable, even if we put a constraint on the payoff of the equilibrium. Our undecidability result holds even for a restricted class of concurrent games, where nonzero rewards occur only on terminal states. Moreover, we show that the constrained existence problem is undecidable not only for concurrent games but for turnbased games with the same restriction on rewards. Finally, we prove that the constrained existence problem for Nash equilibria in (pure or randomised) stationary strategies is decidable and analyse its complexity. 1
Energy games in multiweighted automata
 in: ICTAC’11, vol. 6916 of LNCS
, 2011
"... Abstract. Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g. only for behaviours where a resource is always available (nonnega ..."
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Abstract. Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g. only for behaviours where a resource is always available (nonnegative accumulated weight), yet does not exceed a given maximum capacity. We extend energy games to a multiweighted and parameterized setting, allowing us to model systems with multiple quantitative aspects. We present reductions between Petri nets and multiweighted automata and among different types of multiweighted automata and identify new complexity and (un)decidability results for both one and twoplayer games. We also investigate the tractability of an extension of multiweighted energy games in the setting of timed automata. 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 (2 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
Measuring Permissiveness in Parity Games: MeanPayoff Parity Games Revisited
, 2011
"... We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by a strategy. Using a translation into meanpayoff parity games, we prov ..."
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Cited by 8 (2 self)
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We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by a strategy. Using a translation into meanpayoff parity games, we prove that deciding (the permissiveness of) a most permissive winning strategy is in NP ∩ coNP. Along the way, we provide a new study of meanpayoff parity games. In particular, we give a new algorithm for solving these games, which beats all previously known algorithms for this problem.
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
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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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
Efficient analysis of probabilistic programs with an unbounded counter
 CoRR
"... Abstract. We show that a subclass of infinitestate probabilistic programs that can be modeled by probabilistic onecounter automata (pOC) admits an efficient quantitative analysis. In particular, we show that the expected termination time can be approximated up to an arbitrarily small relative erro ..."
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Cited by 5 (3 self)
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Abstract. We show that a subclass of infinitestate probabilistic programs that can be modeled by probabilistic onecounter automata (pOC) admits an efficient quantitative analysis. In particular, we show that the expected termination time can be approximated up to an arbitrarily small relative error with polynomially many arithmetic operations, and the same holds for the probability of all runs that satisfy a given ωregular property. Further, our results establish a powerful link between pOC and martingale theory, which leads to fundamental observations about quantitative properties of runs in pOC. In particular, we provide a “divergence gap theorem”, which bounds a positive nontermination probability in pOC away from zero. 1
Optimal Bounds for Multiweighted and Parametrised Energy Games
"... Abstract. 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 ..."
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Abstract. 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. 1