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273
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 2651 (32 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.
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 680 (13 self)
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A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on purely discrete state spaces only. In particular, various classes of hybrid automata induce finitary trace equivalence (or similarity, or bisimilarity) relations on an uncountable state space, thus permitting the application of various modelchecking techniques that were originally developed for finitestate systems.
HyTech: A Model Checker for Hybrid Systems
 Software Tools for Technology Transfer
, 1997
"... A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing conti ..."
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Cited by 467 (6 self)
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A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing continuous change. HyTech is a symbolic model checker for linear hybrid automata, a subclass of hybrid automata that can be analyzed automatically by computing with polyhedral state sets. A key feature of HyTech is its ability to perform parametric analysis, i.e. to determine the values of design parameters for which a linear hybrid automaton satisfies a temporallogic requirement. 1 Introduction A hybrid system typically consists of a collection of digital programs that interact with each other and with an analog environment. Examples of hybrid systems include manufacturing controllers, automotive and flight controllers, medical equipment, microelectromechanical systems, and robots. When thes...
Conflict Resolution for Air Traffic Management: A Study in Multiagent Hybrid Systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... Air Traffic Management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this p ..."
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Cited by 277 (50 self)
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Air Traffic Management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe conflict resolution maneuvers. The method models the aircraft and the maneuver as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft. Examples of maneuvers using both speed and heading changes are worked out in detail.
Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 138 (13 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
Approximate Reachability Analysis of PiecewiseLinear Dynamical Systems
, 2000
"... . In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much small ..."
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Cited by 138 (32 self)
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. In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much smaller than in previouslyused methods. The d=dt system can, so far, treat nontrivial continuous systems, hybrid systems, convex differential inclusions and controller synthesis problems. 1 Introduction The problem of calculating reachable states for continuous and hybrid systems has emerged as one of the major problems in hybrid systems research [G96,GM98,DM98,KV97,V98,GM99,CK99,PSK99,HHMW99]. It constitutes a prerequisite for exporting algorithmic verification methodology outside discrete systems or hybrid systems with piecewisetrivial dynamics. For computer scientists it poses new challenges in treating continuous functions and their approximations and in applying computational geometry...
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 121 (2 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...
Automatic verification of realtime systems with discrete probability distributions
 Theoretical Computer Science
, 1999
"... Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the ..."
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Cited by 119 (34 self)
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Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for realtime systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1