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148
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 483 (9 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.
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 251 (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...
A Really Temporal Logic
 Journal of the ACM
, 1989
"... . We introduce a temporal logic for the specification of realtime systems. Our logic, TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier binds a variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable f ..."
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Cited by 238 (26 self)
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. We introduce a temporal logic for the specification of realtime systems. Our logic, TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier binds a variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable formalism for verification. We present a tableaubased decision procedure and a model checking algorithm for TPTL. Several generalizations of TPTL are shown to be highly undecidable. 1 Introduction Linear temporal logic is a widely accepted language for specifying properties of reactive systems and their behavior over time [Pnu77, OL82, MP92]. The tableaubased satisfiability algorithm for its propositional version, PTL, forms the basis for the automatic verification and synthesis of finitestate systems [LP84, MW84]. PTL is interpreted over models that abstract away from the actual times at which events occur, retaining only temporal ordering information about the states of a system. The a...
The Benefits of Relaxing Punctuality
, 1996
"... The most natural, compositional, way of modeling realtime 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 202 (18 self)
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The most natural, compositional, way of modeling realtime 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 EXPSPACEcomplete. This result allows us to develop an algorithm for the verification of timing properties of realtime systems with a dense semantics.
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 202 (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.
What Good Are Digital Clocks?
, 1992
"... . Realtime systems operate in "real," continuous time and state changes may occur at any realnumbered time point. Yet many verification methods are based on the assumption that states are observed at integer time points only. What can we conclude if a realtime system has been shown "correct" ..."
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Cited by 110 (14 self)
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. Realtime systems operate in "real," continuous time and state changes may occur at any realnumbered time point. Yet many verification methods are based on the assumption that states are observed at integer time points only. What can we conclude if a realtime system has been shown "correct" for integral observations? Integer time verification techniques suffice if the problem of whether all realnumbered behaviors of a system satisfy a property can be reduced to the question of whether the integral observations satisfy a (possibly modified) property. We show that this reduction is possible for a large and important class of systems and properties: the class of systems includes all systems that can be modeled as timed transition systems; the class of properties includes timebounded invariance and timebounded response. 1 Introduction Over the past few years, we have seen a proliferation of formal methodologies for software and hardware design that emphasize the treatm...
Design of Embedded Systems: Formal Models, Validation, and Synthesis
 PROCEEDINGS OF THE IEEE
, 1999
"... This paper addresses the design of reactive realtime embedded systems. Such systems are often heterogeneous in implementation technologies and design styles, for example by combining hardware ASICs with embedded software. The concurrent design process for such embedded systems involves solving the ..."
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Cited by 106 (9 self)
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This paper addresses the design of reactive realtime embedded systems. Such systems are often heterogeneous in implementation technologies and design styles, for example by combining hardware ASICs with embedded software. The concurrent design process for such embedded systems involves solving the specification, validation, and synthesis problems. We review the variety of approaches to these problems that have been taken.
The ForSpec Temporal Logic: A New Temporal PropertySpecification Language
, 2001
"... In this paper we describe the ForSpec Temporal Logic (FTL), the new temporal propertyspecification logic of ForSpec, Intel's new formal specification language. The key features of FTL are as follows: it is a linear temporal logic, based on Pnueli's LTL, it is based on a rich set of logical and a ..."
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Cited by 79 (22 self)
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In this paper we describe the ForSpec Temporal Logic (FTL), the new temporal propertyspecification logic of ForSpec, Intel's new formal specification language. The key features of FTL are as follows: it is a linear temporal logic, based on Pnueli's LTL, it is based on a rich set of logical and arithmetical operations on bit vectors to describe state properties, it enables the user to define temporal connectives over time windows, it enables the user to define regular events, which are regular sequences of Boolean events, and then relate such events via special connectives, it enables the user to express properties about the past, and it includes constructs that enable the user to model multiple clock and reset signals, which is useful in the verification of hardware design.
Verifying Hybrid Systems
 In Grossman et al
, 1993
"... . Hybrid systems are modeled as phase transition systems with sampling semantics. By identifying a set of important events it is ensured that all significant state changes are observed, thus correcting previous drawbacks of the sampling computations semantics. A proof rule for verifying properties o ..."
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Cited by 73 (1 self)
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. Hybrid systems are modeled as phase transition systems with sampling semantics. By identifying a set of important events it is ensured that all significant state changes are observed, thus correcting previous drawbacks of the sampling computations semantics. A proof rule for verifying properties of hybrid systems is presented and illustrated on several examples. Keywords: Temporal logic, realtime, specification, verification, hybrid systems, statecharts, proof rules, phase transition system, sampling semantics, important events. 1 Introduction Hybrid systems are reactive systems that intermix discrete and continuous components. Typical examples are digital controllers that interact with continuously changing physical environments. A formal model for hybrid systems was proposed in [MMP92], based on the notion of phase transition systems (PTS). Two types of semantics were considered in [MMP92]. The first semantics, to which we refer here as the super dense semantics, is based on hyb...