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52
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 modelc ..."
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Cited by 90 (26 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.
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 61 (27 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
The Element of Surprise in Timed Games
"... We consider concurrent twoperson games played in real time, in which the players decide both which action to play, and when to play it. Such timed games differ from untimed games in two essential ways. First, players can take each other by surprise, because actions are played with delays that canno ..."
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Cited by 57 (13 self)
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We consider concurrent twoperson games played in real time, in which the players decide both which action to play, and when to play it. Such timed games differ from untimed games in two essential ways. First, players can take each other by surprise, because actions are played with delays that cannot be anticipated by the opponent. Second, a player should not be able to win the game by preventing time from diverging. We present a model of timed games that preserves the element of surprise and accounts for time divergence in a way that treats both players symmetrically and applies to all !regular winning conditions.
A Comparison of Control Problems for Timed and Hybrid Systems
, 2002
"... In the literature, we nd several formulations of the control problem for timed and hybrid systems. We argue that formulations where a controller can cause an action at any point in dense (rational or real) time are problematic, by presenting an example where the controller must act faster and faster ..."
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Cited by 52 (11 self)
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In the literature, we nd several formulations of the control problem for timed and hybrid systems. We argue that formulations where a controller can cause an action at any point in dense (rational or real) time are problematic, by presenting an example where the controller must act faster and faster, yet causes no Zeno eects (say, the control actions are at times 0; 1 2 ; 1; 1 3 4 ; 2; 2 7 8 ; 3; 3 15 16 ; : : :). Such a controller is, of course, not implementable in software. Such controllers are avoided by formulations where the controller can cause actions only at discrete (integer) points in time. While the resulting control problem is wellunderstood if the time unit, or \sampling rate" of the controller, is xed a priori, we dene a novel, stronger formulation: the discretetime control problem with unknown sampling rate asks if a sampling controller exists for some sampling rate. We prove that, surprisingly and unfortunately, this problem is undecidable even in the special case of timed automata. 1
Symbolic models for nonlinear control systems using approximate bisimulation
, 2007
"... Symbolic models for nonlinear control systems using approximate bisimulation Abstract — Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with ..."
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Cited by 42 (12 self)
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Symbolic models for nonlinear control systems using approximate bisimulation Abstract — Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. This has spurred a recent interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each “symbol” corresponds to an “aggregate” of continuous states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provided a unified language to study problems of control in which software and hardware interact with the physical world. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to symbolic model with a precision that can be chosen a–priori. We also show that for digital controlled systems, in which inputs are piecewise–constant, and under the stronger assumption of incremental input–to–state stability, the symbolic models can be obtained, based on a suitable quantization of the inputs.
A.: Timed I/O Automata: A Complete Specification Theory for Realtime Systems
 In: HSCC 2010
, 2010
"... A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation and a set of operators supporting stepwise design. We develop a complete specification framework for realtime systems using Timed I/O Automata as the specification form ..."
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Cited by 34 (15 self)
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A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation and a set of operators supporting stepwise design. We develop a complete specification framework for realtime systems using Timed I/O Automata as the specification formalism, with the semantics expressed in terms of Timed I/O Transition Systems. We provide constructs for refinement, consistency checking, logical and structural composition, and quotient of specifications – all indispensable ingredients of a compositional design methodology. The theory is implemented on top of an engine for timed games, Uppaaltiga, and illustrated with a small case study.
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 30 (5 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
On (Omega)Regular Model Checking
, 2008
"... Checking infinitestate systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transi ..."
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Cited by 14 (4 self)
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Checking infinitestate systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transitions. Among the acceleration techniques that have been proposed, one finds both specific and generic techniques. Specific techniques exploit the particular type of system being analyzed, e.g. a system manipulating queues or integers, whereas generic techniques only assume that the transition relation is represented by a finitestate transducer, which has to be iterated. In this paper, we investigate the possibility of using generic techniques in cases where only specific techniques have been exploited so far. Finding that existing generic techniques are often not applicable in cases easily handled by specific techniques, we have developed a new approach to iterating transducers. This new approach builds on earlier work, but exploits a number of new conceptual and algorithmic ideas, often induced with the help of experiments, that give it a broad scope, as well as good performances.
Control in ominimal hybrid systems
 LICS’06: LOGIC IN COMPUTER SCIENCE
, 2006
"... In this paper, we consider the control of general hybrid systems. Surprisingly, timeabstract bisimulation is not fine enough for solving such a problem. Conversely, we show that suffix equivalence is a correct abstraction for that problem. We apply this equivalence to ominimal hybrid systems and ge ..."
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Cited by 12 (3 self)
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In this paper, we consider the control of general hybrid systems. Surprisingly, timeabstract bisimulation is not fine enough for solving such a problem. Conversely, we show that suffix equivalence is a correct abstraction for that problem. We apply this equivalence to ominimal hybrid systems and get decidability and computability results in this framework.