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578
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 real-time 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 real-time systems. Its definition provides a simple way to annotate state-transition graphs with timing constraints using finitely many real-valued 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 real-time systems.
The algorithmic analysis of hybrid systems
- THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard program-analysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discrete-continuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discrete-continuous state spaces that was previously studied on pur ..."
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Cited by 685 (12 self)
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A hybrid automaton is a formal model for a mixed discrete-continuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discrete-continuous 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 model-checking techniques that were originally developed for finite-state systems.
Alternating-time Temporal Logic
- Journal of the ACM
, 1997
"... Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branching-time temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general var ..."
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Cited by 620 (53 self)
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Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branching-time temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternating-time 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 linear-time and branching-time logics are natural specification languages for closed systems, alternating-time 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 model-checking problems for alternating-time formulas.
Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems
, 1992
"... We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many of the examp ..."
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Cited by 460 (20 self)
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We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many of the examples considered in the workshop can be defined by hybrid automata. While the reachability problem is undecidable even for very restricted classes of hybrid automata, we present two semidecision procedures for verifying safety properties of piecewise-linear hybrid automata, in which all variables change at constant rates. The two procedures are based, respectively, on minimizing and computing fixpoints on generally infinite state spaces. We show that if the procedures terminate, then they give correct answers. We then demonstrate that for many of the typical workshop examples, the procedures do terminate and thus provide an automatic way for verifying their properties. 1 Introduction More and...
What's Decidable about Hybrid Automata?
- Journal of Computer and System Sciences
, 1995
"... . Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify a boundar ..."
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Cited by 377 (16 self)
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. Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify a boundary between decidability and undecidability for the reachability problem of hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow independent trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical significance for verification, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular autom...
The Tool KRONOS
- In Proc. of Hybrid Systems III, LNCS 1066
, 1996
"... KRONOS [6, 8] is a tool developed with the aim to assist the user to validate complex real-time systems. The tool checks whether a real-tinae system modeled by a timed automaton [4] satisfies a timing property specified by a formula of the temporal logic TCTL [3]. KRONOS implements the symbolic mode ..."
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Cited by 270 (41 self)
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KRONOS [6, 8] is a tool developed with the aim to assist the user to validate complex real-time systems. The tool checks whether a real-tinae system modeled by a timed automaton [4] satisfies a timing property specified by a formula of the temporal logic TCTL [3]. KRONOS implements the symbolic model-checking
The Benefits of Relaxing Punctuality
, 1996
"... The most natural, compositional, way of modeling real-time systems uses a dense domain for time. The satis ability of timing constraints that are capable of expressing punctuality in this model, however, is known to be undecidable. We introduce a temporal language that can constrain the time differe ..."
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Cited by 257 (17 self)
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The most natural, compositional, way of modeling real-time systems uses a dense domain for time. The satis ability of timing constraints that are capable of expressing punctuality in this model, however, is known to be undecidable. We introduce a temporal language that can constrain the time difference between events only with finite, yet arbitrary, precision and show the resulting logic to be EXPSPACE-complete. This result allows us to develop an algorithm for the verification of timing properties of real-time systems with a dense semantics.
On the Synthesis of Discrete Controllers for Timed Systems
- in E.W. Mayr and C. Puech (Eds), Proc. STACS'95, LNCS 900
, 1995
"... Abstract. This paper presents algorithms for the automatic synthesis of real-time controllers by nding a winning strategy for certain games de ned by the timed-automata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that thes ..."
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Cited by 243 (18 self)
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Abstract. This paper presents algorithms for the automatic synthesis of real-time controllers by nding a winning strategy for certain games de ned by the timed-automata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that these results will pave theway for the application of program synthesis techniques to the construction of real-time embedded systems from their speci cations. 1
Kronos: A model-checking tool for real-time systems,” in Computer Aided Verification, ser.
- Lecture Notes in Computer Science, A. Hu
, 1998
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