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52
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...
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 203 (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.
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.
Logics and Models of Real Time: A Survey
"... We survey logicbased and automatabased languages and techniques for the specification and verification of realtime systems. In particular, we discuss three syntactic extensions of temporal logic: timebounded operators, freeze quantification, and time variables. We also discuss the extension of ..."
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Cited by 183 (16 self)
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We survey logicbased and automatabased languages and techniques for the specification and verification of realtime systems. In particular, we discuss three syntactic extensions of temporal logic: timebounded operators, freeze quantification, and time variables. We also discuss the extension of finitestate machines with clocks and the extension of transition systems with time bounds on the transitions. All of the resulting notations can be interpreted over a variety of different models of time and computation, including linear and branching time, interleaving and true concurrency, discrete and continuous time. For each choice of syntax and semantics, we summarize the results that are known about expressive power, algorithmic finitestate verification, and deductive verification.
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 147 (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.
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...
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.
TimeConstrained Automata
 CONCUR '91: 2nd International Conference on Concurrency Theory, volume 527 of Lecture Notes in Computer Science
, 1991
"... ) Michael Merritt AT&T Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07974 merritt@research.att.com Francesmary Modugno School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 fmm@cs.cmu.edu Mark R. Tuttle DEC Cambridge Research Lab One Kendall Sq., Bldg. 700 Cambridg ..."
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Cited by 83 (0 self)
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) Michael Merritt AT&T Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07974 merritt@research.att.com Francesmary Modugno School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 fmm@cs.cmu.edu Mark R. Tuttle DEC Cambridge Research Lab One Kendall Sq., Bldg. 700 Cambridge, MA 02139 tuttle@crl.dec.com Abstract In this paper, we augment the inputoutput automaton model in order to reason about time in concurrent systems, and we prove simple properties of this augmentation. The inputoutput automata model is a useful model for reasoning about computation in concurrent and distributed systems because it allows fundamental properties such as fairness and compositionality to be expressed easily and naturally. A unique property of the model is that systems are modeled as the composition of autonomous components. This paper describes a way to add a notion of time to the model in a way that preserves these properties. The result is a simple, compositional model fo...
Timed Transition Systems
, 1992
"... . We incorporate time into an interleaving model of concurrency. In timed transition systems, the qualitative fairness requirements of traditional transition system are replaced (and superseded) by quantitative lowerbound and upperbound timing constraints on transitions. The purpose of this paper i ..."
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Cited by 78 (6 self)
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. We incorporate time into an interleaving model of concurrency. In timed transition systems, the qualitative fairness requirements of traditional transition system are replaced (and superseded) by quantitative lowerbound and upperbound timing constraints on transitions. The purpose of this paper is to explore the scope of applicability for the abstract model of timed transition systems. We demonstrate that the model can represent a wide variety of phenomena that routinely occur in conjunction with the timed execution of concurrent processes. Our treatment covers both processes that are executed in parallel on separate processors and communicate either through shared variables or by message passing, and processes that timeshare a limited number of processors under a given scheduling policy. Often it is this scheduling policy that determines if a system meets its realtime requirements. Thus we explicitly address such questions as timeouts, interrupts, static and dynamic priorities. ...
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...