Results 1  10
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60
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
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
On OmegaLanguages Defined by MeanPayoff Conditions
"... Abstract. In quantitative verification, system states/transitions have associated payoffs, and these are used to associate meanpayoffs with infinite behaviors. In this paper, we propose to define ωlanguages via Boolean queries over meanpayoffs. Requirements concerning averages such as “the number ..."
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Cited by 20 (1 self)
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Abstract. In quantitative verification, system states/transitions have associated payoffs, and these are used to associate meanpayoffs with infinite behaviors. In this paper, we propose to define ωlanguages via Boolean queries over meanpayoffs. Requirements concerning averages such as “the number of messages lost is negligible ” are not ωregular, but specifiable in our framework. We show that, for closure under intersection, one needs to consider multidimensional payoffs. We argue that the acceptance condition needs to examine the set of accumulation points of sequences of meanpayoffs of prefixes, and give a precise characterization of such sets. We propose the class of multithreshold meanpayoff languages using acceptance conditions that are Boolean combinations of inequalities comparing the minimal or maximal accumulation point along some coordinate with a constant threshold. For this class of languages, we study expressiveness, closure properties, analyzability, and Borel complexity. 1
Games where you can play optimally without any memory
 In CONCUR 2005, LNCS
, 2005
"... Abstract. Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently how ..."
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Cited by 19 (6 self)
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Abstract. Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently however also games with other types of payments, like discounted or meanpayoff [5,6], previously used only in economic context, entered into the area of system modelling and verification. The most outstanding property of parity, meanpayoff and discounted games is the existence of optimal positional (memoryless) strategies for both players. This observation raises two questions: (1) can we characterise the family of payoff mappings for which there always exist optimal positional strategies for both players and (2) are there other payoff mappings with practical or theoretical interest and admitting optimal positional strategies. This paper provides a complete answer to the first question by presenting a simple necessary and sufficient condition on payoff mapping guaranteeing the existence of optimal positional strategies. As a corollary to this result we show the following remarkable property of payoff mappings: if both players have optimal positional strategies when playing solitary oneplayer games then also they have optimal positional strategies for twoplayer games.
Pure stationary optimal strategies in Markov decision processes
 In Proc. of STACS’07
, 2006
"... Abstract. Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. Performances of an MDP are evaluated by a payoff function. The controller of the MDP seeks to optimize those performances, using optimal strategies. There exists various ways of measuring ..."
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Cited by 18 (5 self)
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Abstract. Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. Performances of an MDP are evaluated by a payoff function. The controller of the MDP seeks to optimize those performances, using optimal strategies. There exists various ways of measuring performances, i.e. various classes of payoff functions. For example, average performances can be evaluated by a meanpayoff function, peak performances by a limsup payoff function, and the parity payoff function can be used to encode logical specifications. Surprisingly, all the MDPs equipped with mean, limsup or parity payoff functions share a common nontrivial property: they admit pure stationary optimal strategies. In this paper, we introduce the class of prefixindependent and submixing payoff functions, and we prove that any MDP equipped with such a payoff function admits pure stationary optimal strategies. This result unifies and simplifies several existing proofs. Moreover, it is a key tool for generating new examples of MDPs with pure stationary optimal strategies. 1
Optimal Strategy Synthesis For Requestresponse Games
 THEORETICAL INFORMATICS AND APPLICATIONS
, 1999
"... We show the existence and effective computability of optimal winning strategies for requestresponse games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their responses. ..."
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Cited by 15 (3 self)
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We show the existence and effective computability of optimal winning strategies for requestresponse games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their responses.
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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Cited by 12 (4 self)
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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
A constraintbased approach to solving games on infinite graphs
 In POPL
, 2014
"... We present a constraintbased approach to computing winning strategies in twoplayer graph games over the state space of infinitestate programs. Such games have numerous applications in program verification and synthesis, including the synthesis of infinitestate reactive programs and branchingti ..."
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Cited by 12 (5 self)
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We present a constraintbased approach to computing winning strategies in twoplayer graph games over the state space of infinitestate programs. Such games have numerous applications in program verification and synthesis, including the synthesis of infinitestate reactive programs and branchingtime verification of infinitestate programs. Our method handles games with winning conditions given by safety, reachability, and general Linear Temporal Logic (LTL) properties. For each property class, we give a deductive proof rule that — provided a symbolic representation of the game players — describes a winning strategy for a particular player. Our rules are sound and relatively complete. We show that these rules can be automated by using an offtheshelf Horn constraint solver that supports existential quantification in clause heads. The practical promise of the rules is demonstrated through several case studies, including a challenging “CinderellaStepmother game ” that allows infinite alternation of discrete and continuous choices by two players, as well as examples derived from prior work on program repair and synthesis.
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