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68
Optimal strategies in priced timed game automata
 In FSTTCS 04, LNCS 3328
, 2004
"... Abstract. Priced timed (game) automata extend timed (game) automata with costs on both locations and transitions. In this paper we focus on reachability games for priced timed game automata and prove that the optimal cost for winning such a game is computable under conditions concerning the nonzeno ..."
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Cited by 52 (23 self)
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Abstract. Priced timed (game) automata extend timed (game) automata with costs on both locations and transitions. In this paper we focus on reachability games for priced timed game automata and prove that the optimal cost for winning such a game is computable under conditions concerning the nonzenoness of cost and we prove that it is decidable. Under stronger conditions (strictness of constraints) we prove that in case an optimal strategy exists, we can compute a statebased winning optimal strategy. 1
Performance analysis of probabilistic timed automata using digital clocks
 Proc. Formal Modeling and Analysis of Timed Systems (FORMATS’03), volume 2791 of LNCS
, 2003
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Efficient onthefly algorithms for the analysis of timed games
 IN CONCUR 05, LNCS 3653
, 2005
"... In this paper, we propose a first efficient onthefly algorithm for solving games based on timed game automata with respect to reachability and safety properties. The algorithm we propose is a symbolic extension of the onthefly algorithm suggested by Liu & Smolka [15] for lineartime modelcheck ..."
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Cited by 49 (14 self)
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In this paper, we propose a first efficient onthefly algorithm for solving games based on timed game automata with respect to reachability and safety properties. The algorithm we propose is a symbolic extension of the onthefly algorithm suggested by Liu & Smolka [15] for lineartime modelchecking of finitestate systems. Being onthefly, the symbolic algorithm may terminate long before having explored the entire statespace. Also the individual steps of the algorithm are carried out efficiently by the use of socalled zones as the underlying data structure. Various optimizations of the basic symbolic algorithm are proposed as well as methods for obtaining timeoptimal winning strategies (for reachability games). Extensive evaluation of an experimental implementation of the algorithm yields very encouraging performance results.
Staying Alive As Cheaply As Possible
 In Proc. of 7th Intl. Workshop on Hybrid Systems: Computation and Control (HSCC), volume 2993 of Lect. Notes in Comp. Sci
, 2004
"... This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modellin ..."
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Cited by 32 (18 self)
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This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal nonterminating schedules for such doublepriced timed automata is computable.
OptimalReachability and Control for Acyclic Weighted Timed Automata
 Proc. 2nd IFIP International Conference on Theoretical Computer Science (TCS’02
, 2002
"... Weighted timed automata extend timed automata with costs on both locations and transitions. In this framework we study the optimal reachability and the optimal control synthesis problems for the automata with acyclic control graphs. This class of automata is relevant for some practical problems such ..."
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Cited by 25 (2 self)
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Weighted timed automata extend timed automata with costs on both locations and transitions. In this framework we study the optimal reachability and the optimal control synthesis problems for the automata with acyclic control graphs. This class of automata is relevant for some practical problems such as some static scheduling problems or airtraffic control problems. We give a nondeterministic polynomial time algorithm to solve the decision version of the considered optimal reachability problem. This algorithm matches the known lower bound on the reachability for acyclic timed automata, and thus the problem is NPcomplete. We also solve in doubly exponential time the corresponding control synthesis problem. ∗ The first and the second authors were supported in part by the NSF award CCR9970925,
On optimal timed strategies
 In FORMATS 05, LNCS 3829
, 2005
"... Abstract. In this paper, we study timed games played on weighted timed automata. In this context, the reachability problem asks if, given a set T of locations and a cost C, Player 1 has a strategy to force the game into T with a cost less than C no matter how Player 2 behaves. Recently, this problem ..."
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Cited by 23 (4 self)
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Abstract. In this paper, we study timed games played on weighted timed automata. In this context, the reachability problem asks if, given a set T of locations and a cost C, Player 1 has a strategy to force the game into T with a cost less than C no matter how Player 2 behaves. Recently, this problem has been studied independently by Alur et al and by Bouyer et al. In those two works, a semialgorithm is proposed to solve the reachability problem, which is proved to terminate under a condition imposing the nonzenoness of cost. In this paper, we show that in the general case the existence of a strategy for Player 1 to win the game with a bounded cost is undecidable. Our undecidability result holds for weighted timed game automata with five clocks. On the positive side, we show that if we restrict the number of clocks to one and we limit the form of the cost on locations, then the semialgorithm proposed by Bouyer et al always terminates. 1
Linear time logic control of discretetime linear systems
 IEEE Transactions on Automatic Control
, 2006
"... Abstract. The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no ..."
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Cited by 21 (3 self)
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Abstract. The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no longer captured by usual control specifications such as stabilization or output regulation. Instead, we consider specifications given by Linear Temporal Logic (LTL) formulas. We show that existence of controllers for discretetime controllable linear systems and LTL specifications can be decided and that such controllers can be effectively computed. The closedloop system is of hybrid nature, combining the original continuous dynamics with the automatically synthesized switching logic required to enforce the specification. 1.
K.G.: Optimal infinite scheduling for multipriced timed automata
 Formal Methods in System Design 32
, 2008
"... Abstract. This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate m ..."
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Cited by 19 (4 self)
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Abstract. This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal nonterminating schedules for such doublepriced timed automata is computable. This is done by a reduction of the problem to the determination of optimal meancycles in finite graphs with weighted edges. This reduction is obtained by introducing the socalled cornerpoint abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules. 1
Model checking probabilistic timed automata with one or two clocks
 In TACAS 2007, volume 4424 of LNCS
, 2007
"... Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider modelchecking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic modelchecking problems ( ..."
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Cited by 17 (7 self)
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Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider modelchecking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic modelchecking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIMEcomplete for one clock probabilistic timed automata, and are EXPTIMEcomplete for probabilistic timed automata with two clocks. Secondly, we show that the modelchecking problem for the probabilistic timed temporal logic PTCTL is EXPTIMEcomplete for one clock probabilistic timed automata. However, the corresponding modelchecking problem for the subclass of PTCTL which does not permit both (1) punctual timing bounds, which require the occurrence of an event at an exact time point, and (2) comparisons with probability bounds other than 0 or 1, is PTIMEcomplete. 1
Infinite Runs in Weighted Timed Automata with Energy Constraints
"... Abstract. 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 tr ..."
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Cited by 17 (5 self)
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Abstract. 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. 1