## What Good Are Digital Clocks? (1992)

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Citations: | 120 - 15 self |

### BibTeX

@INPROCEEDINGS{Henzinger92whatgood,

author = {Thomas Henzinger and Zohar Manna and Amir Pnueli},

title = {What Good Are Digital Clocks?},

booktitle = {},

year = {1992},

pages = {545--558},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Real-time systems operate in "real," continuous time and state changes may occur at any real-numbered 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 real-time system has been shown "correct" for integral observations? Integer time verification techniques suffice if the problem of whether all real-numbered 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 time-bounded invariance and time-bounded 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...

### Citations

1620 |
A.: The Temporal Logic of Reactive and Concurrent Systems
- Manna, Pnueli
- 1992
(Show Context)
Citation Context ...cases are a minimal delay 0 and a maximal delay 1 for a transitions. While the former does not rule out any computations of S \Gamma , the latter adds to S \Gamma a weak-fairness (justice) assumption =-=[22]-=-:scannot be continuously enabled without being taken. Theorem 2 (Timed transition systems) The set of dense-time computations of a timed transition system is digitizable. Proof. (1) To see that the se... |

1318 |
The temporal logic of programs
- Pnueli
- 1977
(Show Context)
Citation Context ...ense-time properties, by interpreting them over precisely timed state sequences. 3.1 Timed transition systems Timed transition systems generalize the conventional model of discrete transition systems =-=[18, 26]-=- by imposing real-time constraints on the transitions: with each transition we associate a minimal and a maximal delay. We only summarize the formal definition of timed transition systems in this pape... |

443 |
D.,: “Automata for modeling real-time systems
- Alur, Dill
- 1990
(Show Context)
Citation Context ...s of practical interest for two reasons: ffl The dense-time model does not only correspond more closely to the physical reality than the integral-time model, but it is essential for composing systems =-=[1, 6]-=-. ffl Integral-time verification methods are not only significantly simpler than dense-time techniques, but apply to a wider range of real-time properties (because many instances of the dense-time ver... |

266 | LUSTRE: A declarative language for programming synchronous systems
- Caspi, Pilaud, et al.
- 1987
(Show Context)
Citation Context ...ay check if S j= R OE 4 An alternative restriction that allows the inversion of digitization is provided by the more restricted class of synchronous systems, which change states only at integer times =-=[7, 9]-=-. 8 by attempting to prove, instead, that S j= Z OE, which can be done using verification methods that have been developed for integer time. Either semantic techniques, such as model-checking algorith... |

260 | A really temporal logic
- Alur, Henzinger
- 1994
(Show Context)
Citation Context ...m are undecidable) [2, 4]. In addition, a wide variety of integral-time verification methods is readily available for the verification of timed transition systems (including model-checking algorithms =-=[3, 4, 12, 25]-=- and proof systems [13, 15, 25]). Our results prescribe the sound application of these techniques for proving how systems behave in real-numbered time. The paper is organized as follows. In Section 2,... |

230 |
Safety analysis of timing properties in real-time systems
- Jahanian, Mok
- 1986
(Show Context)
Citation Context ...[21]. Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real-time systems and phenomena that arise in practice =-=[1, 3, 15, 17, 20, 23, 25, 27]-=-. Discrete trace models differ significantly in the kinds of systems and phenomena they can capture adequately [5]. These differences are caused by different models of time. We distinguish between ana... |

220 | Real-Time Logics: Complexity and Expressiveness
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- 1992
(Show Context)
Citation Context ...ounded response requirements. Second, we show that even nondigitizable dense-time properties may benefit from integer time verification. For any property OE that is definable in metric temporal logic =-=[4, 19]-=-, we construct a (possibly somewhat weaker) property OE W such that S j= Z OE implies S j= R OE W for every timed transition system S. From this result we derive a scheme for approximating dense-time ... |

218 | The benefits of relaxing punctuality - Alur, Feder, et al. - 1996 |

211 |
Specifying real-time properties with metric temporal logic
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- 1990
(Show Context)
Citation Context ...ounded response requirements. Second, we show that even nondigitizable dense-time properties may benefit from integer time verification. For any property OE that is definable in metric temporal logic =-=[4, 19]-=-, we construct a (possibly somewhat weaker) property OE W such that S j= Z OE implies S j= R OE W for every timed transition system S. From this result we derive a scheme for approximating dense-time ... |

195 | Logics and models of real time: A survey - Alur, Henzinger - 1991 |

174 |
Formal verification of parallel programs
- Keller
(Show Context)
Citation Context ...ense-time properties, by interpreting them over precisely timed state sequences. 3.1 Timed transition systems Timed transition systems generalize the conventional model of discrete transition systems =-=[18, 26]-=- by imposing real-time constraints on the transitions: with each transition we associate a minimal and a maximal delay. We only summarize the formal definition of timed transition systems in this pape... |

127 | Quantitative temporal reasoning
- Emerson, Mok, et al.
- 1990
(Show Context)
Citation Context ...ystem based, automata based, and temporal-logic based languages [3, 4, 5, 12]. This is why many researchers have sacrificed the density of time and given their languages digital-clock interpretations =-=[11, 14, 17, 24, 25, 27]-=-. We follow the same path, but rather than being content with solving the simpler integral-time verification problem, we would like to employ integer time techniques to solve the original dense-time v... |

108 |
Temporal Logic for Real-Time Systems
- Ostroff
- 1989
(Show Context)
Citation Context ...m are undecidable) [2, 4]. In addition, a wide variety of integral-time verification methods is readily available for the verification of timed transition systems (including model-checking algorithms =-=[3, 4, 12, 25]-=- and proof systems [13, 15, 25]). Our results prescribe the sound application of these techniques for proving how systems behave in real-numbered time. The paper is organized as follows. In Section 2,... |

99 |
The Esterel synchronous programming language and its mathematical semantics
- Berry, Cosserat
- 1985
(Show Context)
Citation Context ...ay check if S j= R OE 4 An alternative restriction that allows the inversion of digitization is provided by the more restricted class of synchronous systems, which change states only at integer times =-=[7, 9]-=-. 8 by attempting to prove, instead, that S j= Z OE, which can be done using verification methods that have been developed for integer time. Either semantic techniques, such as model-checking algorith... |

84 | Time constrained automata
- Merritt, Modugno, et al.
- 1991
(Show Context)
Citation Context ...[21]. Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real-time systems and phenomena that arise in practice =-=[1, 3, 15, 17, 20, 23, 25, 27]-=-. Discrete trace models differ significantly in the kinds of systems and phenomena they can capture adequately [5]. These differences are caused by different models of time. We distinguish between ana... |

81 | Pnueli A. Timed transition systems - TA, Manna - 1991 |

77 |
A.: A really abstract concurrent model and its temporal logic
- Barringer, Kuiper, et al.
- 1986
(Show Context)
Citation Context ...s of practical interest for two reasons: ffl The dense-time model does not only correspond more closely to the physical reality than the integral-time model, but it is essential for composing systems =-=[1, 6]-=-. ffl Integral-time verification methods are not only significantly simpler than dense-time techniques, but apply to a wider range of real-time properties (because many instances of the dense-time ver... |

67 | Temporal proof-methodologies for real-time systems
- Henzinger, Manna, et al.
- 1991
(Show Context)
Citation Context ...-time programming languages L I and real-time specification languages L S all of whose expressions are digitizable have been proposed in the literature. We show that (1) every timed transition system =-=[15]-=- is digitizable and (2) every qualitative (time-independent) property and the most common quantitative (hard real-time) properties are digitizable. Timed transition systems can model sets of real-time... |

64 |
Explicit clock temporal logic
- Harel, Lichtenstein, et al.
- 1990
(Show Context)
Citation Context ...m are undecidable) [2, 4]. In addition, a wide variety of integral-time verification methods is readily available for the verification of timed transition systems (including model-checking algorithms =-=[3, 4, 12, 25]-=- and proof systems [13, 15, 25]). Our results prescribe the sound application of these techniques for proving how systems behave in real-numbered time. The paper is organized as follows. In Section 2,... |

39 |
Applications of Temporal Logic to the Specification of Real Time
- Pnueli, Harel
- 1988
(Show Context)
Citation Context ...[21]. Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real-time systems and phenomena that arise in practice =-=[1, 3, 15, 17, 20, 23, 25, 27]-=-. Discrete trace models differ significantly in the kinds of systems and phenomena they can capture adequately [5]. These differences are caused by different models of time. We distinguish between ana... |

37 | Using mappings to prove timing properties
- Lynch, Attiya
- 1992
(Show Context)
Citation Context |

35 |
The temporal specification and verification of real-time systems
- Henzinger
- 1991
(Show Context)
Citation Context ...ystem based, automata based, and temporal-logic based languages [3, 4, 5, 12]. This is why many researchers have sacrificed the density of time and given their languages digital-clock interpretations =-=[11, 14, 17, 24, 25, 27]-=-. We follow the same path, but rather than being content with solving the simpler integral-time verification problem, we would like to employ integer time techniques to solve the original dense-time v... |

30 | Half-order modal logic: How to prove real-time properties
- Henzinger
- 1990
(Show Context)
Citation Context ...ition, a wide variety of integral-time verification methods is readily available for the verification of timed transition systems (including model-checking algorithms [3, 4, 12, 25] and proof systems =-=[13, 15, 25]-=-). Our results prescribe the sound application of these techniques for proving how systems behave in real-numbered time. The paper is organized as follows. In Section 2, we introduce both integraltime... |

30 |
ATP, an algebra for timed processes
- Nicollin, Richier, et al.
(Show Context)
Citation Context ...ystem based, automata based, and temporal-logic based languages [3, 4, 5, 12]. This is why many researchers have sacrificed the density of time and given their languages digital-clock interpretations =-=[11, 14, 17, 24, 25, 27]-=-. We follow the same path, but rather than being content with solving the simpler integral-time verification problem, we would like to employ integer time techniques to solve the original dense-time v... |

20 |
The bene ts of relaxing punctuality
- Alur, Feder, et al.
- 1991
(Show Context)
Citation Context ...methods are not only signi cantly simpler than dense-time techniques, but apply to a wider range of real-time properties (because many instances of the dense-time veri cation problem are undecidable) =-=[2, 4]-=-. In addition, a wide variety ofintegral-time veri cation methods is readily available for the veri cation of timed transition systems (including model-checking algorithms [3, 4, 12, 25] and proof sys... |

8 |
Applications of temporal logic to the speci cation of real-time systems
- Pnueli, Harel
- 1988
(Show Context)
Citation Context ...[21]. Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real-time systems and phenomena that arise in practice =-=[1, 3,15, 17, 20, 23, 25, 27]-=-. Discrete trace models di er signi cantly in the kinds of systems and phenomena they can capture adequately [5]. These di erences are caused by di erent models of time. We distinguish between analog-... |

6 |
The Temporal Speci cation and Veri cation of Real-time Systems
- Henzinger
- 1991
(Show Context)
Citation Context ...system based, automata based, and temporal-logic based languages [3, 4, 5, 12]. This is why many researchers have sacri ced the density of time and given their languages digital-clock interpretations =-=[11, 14,17, 24, 25, 27]-=-. We follow the same path, but rather than being content with solving the simpler integral-time veri cation problem, we would like to employinteger time techniques to solve the original dense-time ver... |

6 |
Formal veri cation of parallel programs
- Keller
- 1976
(Show Context)
Citation Context ...dense-time properties, byinterpreting them over precisely timed state sequences. 3.1 Timed transition systems Timed transition systems generalize the conventional model of discrete transition systems =-=[18, 26]-=-by imposing real-time constraints on the transitions: with each transition we associate a minimal and a maximal delay. We only summarize the formal de nition of timed transition systems in this paper�... |

3 |
A formal approach to hybrid systems
- Maler, Manna, et al.
- 1992
(Show Context)
Citation Context ...between any two points in time. While the behavior of a discrete process can be described completely by an !-sequence of state changes, more refined models are necessary to study continuous processes =-=[21]-=-. Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real-time systems and phenomena that arise in practice [1, ... |

1 |
Approximating continuous time. Presented at the
- Burch
- 1991
(Show Context)
Citation Context ...e trace models have obvious limitations: 1 Recently it has been brought to the authors' attention that a conservative approximation of real-numbered time by integer time was proposed independently by =-=[8]-=-. 3 Trace (or linear-time) models abstract information about internal decisions of a system. More refined (branching-time) models are necessary to study the internal branching structure of a system [5... |

1 |
Half-order modal logic: howtoprove real-time properties
- Henzinger
- 1990
(Show Context)
Citation Context ...addition, a wide variety ofintegral-time veri cation methods is readily available for the veri cation of timed transition systems (including model-checking algorithms [3, 4, 12, 25] and proof systems =-=[13, 15, 25]-=-). Our results prescribe the sound application of these techniques for proving how systems behave in real-numbered time. The paper is organized as follows. In Section 2, we introduce both integraltime... |

1 |
A formal approach tohybrid systems
- Maler, Manna, et al.
- 1992
(Show Context)
Citation Context ... between any two points in time. While the behavior of a discrete process can be described completely by an !-sequence of state changes, more re ned models are necessary to study continuous processes =-=[21]-=-. Despite (or, often, because of) these limitations, discrete trace models have been used successfully for the analysis of a wide variety of real-time systems and phenomena that arise in practice [1, ... |