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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 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...
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.
A Process Algebra of Communicating Shared Resources with Dense Time and Priorities
 THEORETICAL COMPUTER SCIENCE
, 1997
"... ..."
Temporal Proof Methodologies for Timed Transition Systems
 INFORMATION AND COMPUTATION
, 1994
"... We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with realtime properties of reactive systems. The abstract notion of timed transition systems generalizes traditional transition systems conservatively: ..."
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Cited by 44 (8 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 reactive systems. The abstract notion of timed transition systems generalizes traditional transition systems conservatively: qualitative fairness requirements are replaced (and superseded) by quantitative lowerbound and upperbound timing constraints on transitions. This framework can model realtime systems that communicate either through shared variables or by message passing and realtime issues such as timeouts, process priorities (interrupts), and process scheduling. We exhibit two styles for the specification of realtime systems. While the first approach uses timebounded versions of the temporal operators, the second approach allows explicit references to time through a special clock variable. Corresponding to the two styles of specification, we present and compare two different proof methodologies for t...
Formal Methods for the Specification and Design of RealTime Safety Critical Systems
, 1992
"... Safety critical computers increasingly a#ect nearly every aspect of our lives. Computers control the planes we #y on, monitor our health in hospitals and do our work in hazardous environments. Computers with software de#ciencies that fail to meet stringent timing constraints have resulted in cat ..."
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Cited by 31 (0 self)
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Safety critical computers increasingly a#ect nearly every aspect of our lives. Computers control the planes we #y on, monitor our health in hospitals and do our work in hazardous environments. Computers with software de#ciencies that fail to meet stringent timing constraints have resulted in catastrophic failures. This paper surveys formal methods for specifying, designing and verifying realtime systems, so as to improve their safety and reliability. # To appear in Journal of Systems and Software,Vol. 18, Number 1, pages 33#60, April 1992. Jonathan Ostro# is with the Department of Computer Science, York University 4700 Keele Street, North York, Ontario, Canada, M3J 1P3. This work is supported by the Natural Sciences and Engineering Research Council of Canada. 1 CONTENTS 2 Contents 1 Introduction 3 2 De#ning the terms 6 2.1 Major issues that formal theories must address ::::::: 13 3 RealTime Programming Languages 14 4 Structured Methods and#or Graphical Languages 15 4.1 Str...
Time Bounds for RealTime Process Control in the Presence of Timing Uncertainty
, 1994
"... this paper appeared in "Proceedings of the 10th IEEE RealTime Systems Symposium, Santa Monica, December 1989," pp. 268284. This work was supported by ONR Contract N0001485K~0168, by NSF Contract CCR8611442, and by DARPA Contracts N0001483K0125 and N0001489J1988 ..."
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Cited by 30 (13 self)
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this paper appeared in "Proceedings of the 10th IEEE RealTime Systems Symposium, Santa Monica, December 1989," pp. 268284. This work was supported by ONR Contract N0001485K~0168, by NSF Contract CCR8611442, and by DARPA Contracts N0001483K0125 and N0001489J1988
Specification and Verification of Faulttolerance, Timing and Scheduling
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1999
"... Faulttolerance and timing have often been considered to be implementation issues of a program, quite distinct from the functional safety and liveness properties. Recent work has shown how these nonfunctional and functional properties can be verified in a similar way. However, the more practical qu ..."
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Cited by 17 (5 self)
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Faulttolerance and timing have often been considered to be implementation issues of a program, quite distinct from the functional safety and liveness properties. Recent work has shown how these nonfunctional and functional properties can be verified in a similar way. However, the more practical question of determining whether a realtime program will meet its deadlines, i.e. showing that there is a feasible schedule, is usually done using scheduling theory, quite separately from the verification of other properties of the program. This makes it hard to use the results of scheduling analysis in the design, or redesign, of faulttolerant, realtime programs. This paper shows how faulttolerance, timing and schedulability can be specified and verified using a single notation and model. This allows a unified view to be taken of the functional and nonfunctional properties of programs and a simple transformational method to be used to combine these properties. It also permits results fro...
Multivalued Possibilities Mappings
 Stepwise Refinement of Distributed Systems, volume LNCS 430
, 1989
"... Abstraction mappings are one of the major tools used to construct correctness proofs for concurrent algorithms. Several examples axe given of situations in which it is useful to allow the abstraction mappings to be multivalued, The examples involve algorithm optimization, algorithm distribution, and ..."
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Cited by 13 (2 self)
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Abstraction mappings are one of the major tools used to construct correctness proofs for concurrent algorithms. Several examples axe given of situations in which it is useful to allow the abstraction mappings to be multivalued, The examples involve algorithm optimization, algorithm distribution, and proofs of time bounds.