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29
Infinite Runs in Weighted Timed Automata with Energy Constraints
"... We study the problems of existence and construction of infinite schedules for finite weighted automata and oneclock weighted timed automata, subject to boundary constraints on the accumulated weight. More specifically, we consider automata equipped with positive and negative weights on transitions ..."
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Cited by 42 (12 self)
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We study the problems of existence and construction of infinite schedules for finite weighted automata and oneclock weighted timed automata, subject to boundary constraints on the accumulated weight. More specifically, we consider automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource (e.g. energy). We ask the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints (e.g. remains between 0 and some given upperbound). We also consider a game version of the above, where certain transitions may be uncontrollable.
Reachabilitytime games on timed automata
 In Proc. of 34th Int. Colloquium on Automata, Languages and Programming (ICALP’07), LNCS 4596
, 2007
"... In a reachabilitytime game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachabilitytime games on strongly nonZeno timed automata using a value iteration algorithm. T ..."
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Cited by 16 (5 self)
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In a reachabilitytime game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachabilitytime games on strongly nonZeno timed automata using a value iteration algorithm. This paper complements their work by providing a strategy improvement algorithm for the problem. It also generalizes their decidability result because the proposed strategy improvement algorithm solves reachabilitytime games on all timed automata. The exact computational complexity of solving reachabilitytime games is also established: the problem is EXPTIMEcomplete for timed automata with at least two clocks. 1
Nash equilibria for reachability objectives in multiplayer timed games
 LAB. SPÉCIFICATION & VÉRIFICATION, ENS
, 2010
"... We propose a procedure for computing Nash equilibria in multiplayer timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use ..."
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Cited by 10 (6 self)
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We propose a procedure for computing Nash equilibria in multiplayer timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use our characterization to compute Nash equilibria in finite concurrent games.
DiscreteTime Verification and Control for Probabilistic Rectangular Hybrid Automata
"... Abstract—Hybrid automata provide a modeling formalism for systems characterized by a combination of discrete and continuous components. Probabilistic rectangular automata generalize the class of rectangular hybrid automata with the possibility of representing random behavior of the discrete componen ..."
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Cited by 6 (2 self)
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Abstract—Hybrid automata provide a modeling formalism for systems characterized by a combination of discrete and continuous components. Probabilistic rectangular automata generalize the class of rectangular hybrid automata with the possibility of representing random behavior of the discrete components of the system. We consider the following two problems regarding probabilistic rectangular automata: verification concerns the computation of the maximum probability with which the system can satisfy a certain ωregular specification; control concerns the computation of a strategy which guides certain choices of the system in order to maximize the probability of satisfying a certain ωregular specification. Our main contribution is to give algorithms for the verification and control problems for probabilistic rectangular automata in a semantics in which discrete control transitions can occur only at integer points in time. Additionally, we give algorithms for verification of ωregular specifications of probabilistic timed automata, a subclass of probabilistic rectangular automata, with the usual densetime semantics. I.
Nash equilibria in concurrent games with Büchi objectives
 In FSTTCS’11, LIPIcs
, 2011
"... We study the problem of computing purestrategy Nash equilibria in multiplayer concurrent games with Büchidefinable objectives. First, when the objectives are Büchi conditions on the game, we prove that the existence problem can be solved in polynomial time. In a second part, we extend our techniqu ..."
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Cited by 6 (3 self)
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We study the problem of computing purestrategy Nash equilibria in multiplayer concurrent games with Büchidefinable objectives. First, when the objectives are Büchi conditions on the game, we prove that the existence problem can be solved in polynomial time. In a second part, we extend our technique to objectives defined by deterministic Büchi automata, and prove that the problem then becomes EXPTIMEcomplete. We prove PSPACEcompleteness for the case where the Büchi automata are 1weak.
CONCAVELYPRICED PROBABILISTIC TIMED AUTOMATA
"... Concavelypriced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavelypriced probabilistic timed automata for arbitrary initial states. We prove that these pro ..."
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Cited by 5 (4 self)
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Concavelypriced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavelypriced probabilistic timed automata for arbitrary initial states. We prove that these problems are EXPTIMEcomplete for probabilistic timed automata with two or more clocks and PTIMEcomplete for automata with one clock. Previous work on expected price problems for probabilistic timed automata was restricted to expected reachability for linearlypriced automata and integer valued initial states. This work uses the boundary region graph introduced by Jurdziński and Trivedi to analyse properties of concavelypriced (nonprobabilistic) timed automata.
AverageTime Games
 FSTTCS 2008
, 2008
"... ABSTRACT. An averagetime game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimize the average time per transition and playe ..."
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Cited by 4 (3 self)
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ABSTRACT. An averagetime game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimize the average time per transition and player Max wants to maximize it. A solution of averagetime games is presented using a reduction to averageprice game on a finite graph. A direct consequence is an elementary proof of determinacy for averagetime games. This complements our results for reachabilitytime games and partially solves a problem posed by Bouyer et al., to design an algorithm for solving averageprice games on priced timed automata. The paper also establishes the exact computational complexity of solving averagetime games: the problem is EXPTIMEcomplete for timed automata with at least twoclocks.
Expected ReachabilityTime Games
"... Abstract. In an expected reachabilitytime game (ERTG) two players, Min and Max, move a token along the transitions of a probabilistic timed automaton, so as to minimise and maximise, respectively, the expected time to reach a target. These games are concurrent since at each step of the game both pl ..."
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Cited by 3 (1 self)
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Abstract. In an expected reachabilitytime game (ERTG) two players, Min and Max, move a token along the transitions of a probabilistic timed automaton, so as to minimise and maximise, respectively, the expected time to reach a target. These games are concurrent since at each step of the game both players choose a timed move (a time delay and action under their control), and the transition of the game is determined by the timed move of the player who proposes the shorter delay. A game is turnbased if at any step of the game, all available actions are under the control of precisely one player. We show that while concurrent ERTGs are not always determined, turnbased ERTGs are positionally determined. Using the boundary region graph abstraction, and a generalisation of Asarin and Maler’s simple function, we show that the decision problems related to computing the upper/lower values of concurrent ERTGs, and computing the value of turnbased ERTGs are decidable and their complexity is in NEXPTIME ∩ coNEXPTIME. 1
Computing quantiles in Markov reward models
 In Proc. of FOSSACS, LNCS 7794
, 2013
"... Abstract. Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, nam ..."
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Abstract. Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p ∈]0, 1] and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are wellknown from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discretetime finitestate Markov decision processes with nonnegative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in pseudopolynomial time. 1