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59
A theory of timed automata
, 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
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Cited by 1978 (31 self)
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Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of realtime systems whose correctness depends on relative magnitudes of different delays. Consequently, timed automata [7] were introduced as a formal notation to model the behavior of realtime systems. Its definition provides a simple way to annotate statetransition graphs with timing constraints using finitely many realvalued clock variables. Automated analysis of timed automata relies on the construction of a finite quotient of the infinite space of clock valuations. Over the years, the formalism has been extensively studied leading to many results establishing connections to circuits and logic, and much progress has been made in developing verification algorithms, heuristics, and tools. This paper provides a survey of the theory of timed automata, and their role in specification and verification of realtime systems.
Alternatingtime Temporal Logic
 Journal of the ACM
, 1997
"... Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general var ..."
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Cited by 448 (47 self)
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Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternatingtime temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves. While lineartime and branchingtime logics are natural specification languages for closed systems, alternatingtime logics are natural specification languages for open systems. For example, by preceding the temporal operator "eventually" with a selective path quantifier, we can specify that in the game between the system and the environment, the system has a strategy to reach a certain state. Also the problems of receptiveness, realizability, and controllability can be formulated as modelchecking problems for alternatingtime formulas.
ModelChecking in Dense Realtime
 INFORMATION AND COMPUTATION
, 1993
"... Modelchecking is a method of verifying concurrent systems in which a statetransition graph model of the system behavior is compared with a temporal logic formula. This paper extends modelchecking for the branchingtime logic CTL to the analysis of realtime systems, whose correctness depends on t ..."
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Cited by 250 (6 self)
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Modelchecking is a method of verifying concurrent systems in which a statetransition graph model of the system behavior is compared with a temporal logic formula. This paper extends modelchecking for the branchingtime logic CTL to the analysis of realtime systems, whose correctness depends on the magnitudes of the timing delays. For specifications, we extend the syntax of CTL to allow quantitative temporal operators such as 93!5 , meaning "possibly within 5 time units." The formulas of the resulting logic, Timed CTL (TCTL), are interpreted over continuous computation trees, trees in which paths are maps from the set of nonnegative reals to system states. To model finitestate systems we introduce timed graphs  statetransition graphs annotated with timing constraints. As our main result, we develop an algorithm for modelchecking, for determining the truth of a TCTLformula with respect to a timed graph. We argue that choosing a dense domain instead of a discrete domain to mo...
Parametric realtime reasoning
 IN PROCEEDINGS OF THE 25TH ANNUAL SYMPOSIUM ON THEORY OF COMPUTING
, 1993
"... Traditional approaches to the algorithmic verification of realtime systems are limited to checking program correctness with respect to concrete timing properties (e.g., "message delivery within 10 milliseconds"). We address the more realistic and more ambitious problem of deriving symbolic constrai ..."
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Cited by 96 (6 self)
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Traditional approaches to the algorithmic verification of realtime systems are limited to checking program correctness with respect to concrete timing properties (e.g., "message delivery within 10 milliseconds"). We address the more realistic and more ambitious problem of deriving symbolic constraints on the timing properties required of realtime systems (e.g., "message delivery within the time it takes to execute two assignment statements"). To model this problem, we introduce parametric timed automata  finitestate machines whose transitions are constrained with parametric timing requirements. The emptiness question for parametric timed automata is central to the verification problem. On the negative side, we show that in general this question is undecidable. On the positive side, we provide algorithms for checking the emptiness of restricted classes of parametric timed automata. The practical relevance of these classes is illustrated with several verification examples. There remains a gap between the automata classes for which we know that emptiness is decidable and undecidable, respectively, and this gap is related to various hard and open problems of logic and automata theory.
EventClock Automata: A Determinizable Class of Timed Automata
 Theoretical Computer Science
, 1999
"... We introduce eventrecording automata. An eventrecording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of eventrecording automata is, on one hand, expressive enough to model (finite) timed transition systems an ..."
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Cited by 87 (3 self)
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We introduce eventrecording automata. An eventrecording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of eventrecording automata is, on one hand, expressive enough to model (finite) timed transition systems and, on the other hand, determinizable and closed under all boolean operations. As a result, the language inclusion problem is decidable for eventrecording automata. We present a translation from timed transition systems to eventrecording automata, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors. We also consider eventpredicting automata, which contain clocks that predict the time of the next occurrence of an event. The class of eventclock automata, which contain both eventrecording and eventpredicting clocks, is a suitable specification language for realtime properties. We provide an algorithm for checking if a timed automa...
Optimal Paths in Weighted Timed Automata
 HSCC
, 2001
"... We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed gr ..."
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Cited by 84 (6 self)
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We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed graph we construct is a refinement of the region automaton due to Alur and Dill. We present an exponential time algorithm to solve the shortestpath problem for weighted timed automata starting from a single state, and a doublyexponential time algorithm to solve this problem starting from a zone of the state space.
An Implementation of Three Algorithms for Timing Verification Based on Automata Emptiness
, 1992
"... This papers describes modifications to and the implementation of algorithms previously described in [1, 11]. We first describe three generic (untimed) algorithms for constructing graphs of the reachable states of a system, and how these graphs can be used for verification. They all have as input an ..."
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Cited by 57 (3 self)
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This papers describes modifications to and the implementation of algorithms previously described in [1, 11]. We first describe three generic (untimed) algorithms for constructing graphs of the reachable states of a system, and how these graphs can be used for verification. They all have as input an implicit description of a transition system. We then apply these algorithms to realtime systems. The first algorithm performs a straightforward reachability analysis on sets of states of the system, rather than on individual states. This corresponds to stepping symbolically through the system many states at a time. In the case of a realtime system this procedure constructs a graph where each node is the union of some regions of the regions graph. There is therefore no need for an a priori partitioning of the state space into individual regions; however, this approach potentially leads to exponentially worse complexity since its potential state space is the power set of regions [1]. The other two algorithms we consider are minimization algorithms [12, 13, 11]. These simultaneously perform reachability analysis and minimization from an implicit system description. These can lead to great savings when the minimized graph is much smaller than the explicit reachable graph. Our paradigm for verification is to test for the emptiness of the set of all timed system executions that violate a requirements specification. One way to specify and verify nonterminating processes is to model them as languages of !sequences of events [14, 15, 16, 1, 17, 18]. Modular processes can be constructed via composition operations involving language intersection. Specifications are also given as languages: they contain all acceptable event sequences. Program correctness is then just language contain...
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 49 (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
JobShop Scheduling using Timed Automata
, 2001
"... . In this paper we show how the classical jobshop scheduling problem can be modeled as a special class of acyclic timed automata. Finding an optimal schedule corresponds, then, to finding a shortest (in terms of elapsed time) path in the timed automaton. This representation provides new techniq ..."
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Cited by 41 (8 self)
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. In this paper we show how the classical jobshop scheduling problem can be modeled as a special class of acyclic timed automata. Finding an optimal schedule corresponds, then, to finding a shortest (in terms of elapsed time) path in the timed automaton. This representation provides new techniques for solving the optimization problem and, more importantly, it allows to model naturally more complex dynamic resource allocation problems which are not captured so easily in traditional models of operation research. We present several algorithms and heuristics for finding the shortest paths in timed automata and test their implementation in the tool Kronos on numerous benchmark examples. 1