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226
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 685 (12 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.
UPPAAL in a Nutshell
, 1997
"... . This paper presents the overall structure, the design criteria, and the main features of the tool box Uppaal. It gives a detailed user guide which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a realtime system, to simulate its dynamical behavior, ..."
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Cited by 662 (51 self)
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. This paper presents the overall structure, the design criteria, and the main features of the tool box Uppaal. It gives a detailed user guide which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a realtime system, to simulate its dynamical behavior, to specify and verify its safety and bounded liveness properties in terms of its model. In addition, the paper also provides a short review on casestudies where Uppaal is applied, as well as references to its theoretical foundation. 1 Introduction Uppaal is a tool box for modeling, simulation and verification of realtime systems, based on constraintsolving and onthefly techniques, developed jointly by Uppsala University and Aalborg University. It is appropriate for systems that can be modeled as a collection of nondeterministic processes with finite control structure and realvalued clocks, communicating through channels and (or) shared variables [34, 26]. Typical application areas in...
Realtime logics: complexity and expressiveness
 INFORMATION AND COMPUTATION
, 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
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Cited by 252 (16 self)
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The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of realtime logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary realtime temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableaubased decision procedures for checking validity. Consequently, these two formalisms are wellsuited for the speci cation and veri cation of realtime systems.
UPPAAL  a Tool Suite for Automatic Verification of RealTime Systems
, 1996
"... . Uppaal is a tool suite for automatic verification of safety and bounded liveness properties of realtime systems modeled as networks of timed automata. It includes: a graphical interface that supports graphical and textual representations of networks of timed automata, and automatic transformation ..."
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Cited by 244 (15 self)
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. Uppaal is a tool suite for automatic verification of safety and bounded liveness properties of realtime systems modeled as networks of timed automata. It includes: a graphical interface that supports graphical and textual representations of networks of timed automata, and automatic transformation from graphical representations to textual format, a compiler that transforms a certain class of linear hybrid systems to networks of timed automata, and a modelchecker which is implemented based on constraintsolving techniques. Uppaal also supports diagnostic modelchecking providing diagnostic information in case verification of a particular realtime systems fails. The current version of Uppaal is available on the World Wide Web via the Uppaal home page http://www.docs.uu.se/docs/rtmv/uppaal. 1 Introduction Uppaal is a new tool suite for automatic verification of safety and bounded liveness properties of networks of timed automata [13, 8, 6]. The tool was developed during the spring ...
From Timed to Hybrid Systems
"... We propose a framework for the formal speci cation and veri cation of timed and hybrid systems. For timed systems we propose a speci cation language that refers to time only through age functions which measure the length of the most recent timeinterval in which agiven formula has been continuously t ..."
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Cited by 173 (16 self)
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We propose a framework for the formal speci cation and veri cation of timed and hybrid systems. For timed systems we propose a speci cation language that refers to time only through age functions which measure the length of the most recent timeinterval in which agiven formula has been continuously true. We then consider hybrid systems, which are systems consisting of a nontrivial mixture of discrete and continuous components, such as a digital controller that controls acontinuous environment. The proposed framework extends the temporal logic approach which has proven useful for the formal analysis of discrete systems such as reactive programs. The new framework consists of a semantic model for hybrid time, the notion of phase transition systems, which extends the formalism of discrete transition systems, an extended version of Statecharts for the speci cation of hybrid behaviors, and an extended version of temporal logic that enables reasoning about continuous change.
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 symboli ..."
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Cited by 146 (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.