Results 1  10
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20
Better quality in synthesis through quantitative objectives
 In CoRR, abs/0904.2638
, 2009
"... Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation tha ..."
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Cited by 57 (18 self)
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Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the “goodness ” of an implementation. Using games with corresponding quantitative objectives, we can synthesize “optimal ” implementations, which are preferred among the set of possible implementations that satisfy a given specification. In particular, we show how automata with lexicographic meanpayoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic meanpayoff games (for safety requirements), and the solution of games with both lexicographic meanpayoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games. 1
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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Cited by 44 (11 self)
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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
Measuring and synthesizing systems in probabilistic environments
 CoRR
"... Abstract. Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is pre ..."
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Cited by 22 (11 self)
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Abstract. Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimalsynthesis problem: given an omegaregular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the given input assumption, synthesize a system that optimizes the measured value. For safety specifications and measures that are defined by meanpayoff automata, the optimalsynthesis problem amounts to finding a strategy in a Markov decision process (MDP) that is optimal for a longrun average reward objective, which can be done in polynomial time. For general omegaregular specifications, the solution rests on a new, polynomialtime algorithm for computing optimal strategies in MDPs with meanpayoff parity objectives. We present some experimental results showing optimal systems that were automatically generated in this way. 1
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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Cited by 21 (10 self)
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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.
Energy and meanpayoff games with imperfect information
 In CSL 2010, volume LNCS 6247
, 2010
"... Abstract. We consider twoplayer games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resour ..."
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Cited by 18 (2 self)
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Abstract. We consider twoplayer games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resource consumption and the objective of the game is to maintain the sum of weights always nonnegative. In a meanpayoff game, the objective is to optimize the limitaverage usage of the resource. We show that the problem of determining if an energy game with imperfect information with fixed initial credit has a winning strategy is decidable, while the question of the existence of some initial credit such that the game has a winning strategy is undecidable. This undecidability result carries over to meanpayoff games with imperfect information. On the positive side, using a simple restriction on the game graph (namely, that the weights are visible), we show that these problems become EXPTIMEcomplete. 1
MeanPayoff Automaton Expressions
"... Quantitative languages are an extension of boolean languages that assign to each word a real number. Meanpayoff automata are finite automata with numerical weights on transitions that assign to each infinite path the longrun average of the transition weights. When the mode of branching of the aut ..."
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Cited by 11 (4 self)
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Quantitative languages are an extension of boolean languages that assign to each word a real number. Meanpayoff automata are finite automata with numerical weights on transitions that assign to each infinite path the longrun average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating meanpayoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by meanpayoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Meanpayoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating meanpayoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as meanpayoff automaton expressions.
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 11 (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
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