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34
A Logic for Reasoning about Time and Reliability
 Formal Aspects of Computing
, 1994
"... We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted ove ..."
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Cited by 247 (1 self)
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We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and This research report is a revised and extended version of a paper that has appeared under the title "A Framework for Reasoning about Time and Reliability" in the Proceeding of the 10 th IEEE Realtime Systems Symposium, Santa Monica CA, December 1989. This work was partially supported by the Swedish Board for Technical Development (STU) as part of Esprit BRA Project SPEC, and by the Swedish Telecommunication Administration. the Markov chain. A simple example is inc...
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 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.
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 184 (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 146 (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...
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 77 (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. ...
Compiling RealTime Specifications into Extended Automata
 IEEE Transactions on Software Engineering
, 1992
"... We propose a method for the implementation and analysis of realtime systems, based on the compilation of specifications into extended automata. Such a method has been already adopted for the so called "synchronous" realtime programming languages. ..."
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Cited by 75 (8 self)
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We propose a method for the implementation and analysis of realtime systems, based on the compilation of specifications into extended automata. Such a method has been already adopted for the so called "synchronous" realtime programming languages.
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...
Temporal Proof Methodologies for Realtime Systems
 In Proceedings of the 18th Annual Symposium on Principles of Programming Languages
, 1991
"... . We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with realtime properties of concurrent and reactive systems. A global, discrete, and asynchronous clock is incorporated into the model by defining the a ..."
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Cited by 63 (11 self)
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. We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with realtime properties of concurrent and reactive systems. A global, discrete, and asynchronous clock is incorporated into the model by defining the abstract notion of a realtime transition system as a conservative extension of traditional transition systems: qualitative fairness requirements are replaced (and superseded) by quantitative lowerbound and upperbound realtime requirements for transitions. We show how to model realtime systems that communicate either through shared variables or by message passing, and how to represent the important realtime constructs of priorities (interrupts), scheduling, and timeouts in this framework. Two styles for the specification of realtime properties are presented. The first style uses bounded versions of the temporal operators; the realtime requirements expressed in this style are classified ...