## Model-Checking in Dense Real-time (1993)

Venue: | INFORMATION AND COMPUTATION |

Citations: | 266 - 7 self |

### BibTeX

@ARTICLE{Alur93model-checkingin,

author = {Rajeev Alur and Costas Courcoubetis and David Dill},

title = {Model-Checking in Dense Real-time},

journal = {INFORMATION AND COMPUTATION},

year = {1993},

volume = {104},

pages = {2--34}

}

### Years of Citing Articles

### OpenURL

### Abstract

Model-checking is a method of verifying concurrent systems in which a state-transition graph model of the system behavior is compared with a temporal logic formula. This paper extends model-checking for the branching-time logic CTL to the analysis of real-time 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 --- state-transition graphs annotated with timing constraints. As our main result, we develop an algorithm for model-checking, for determining the truth of a TCTL-formula with respect to a timed graph. We argue that choosing a dense domain instead of a discrete domain to mo...

### Citations

1237 | Automatic verification of finite-state concurrent systems using temporallogic specificaitons
- Clarke, Emerson, et al.
- 1986
(Show Context)
Citation Context ...iciency: modelchecking is linear in the product of the size of the state-transition graph and the size of the formula, when the logic is the branching-time temporal logic CTL (computation tree logic) =-=[12]-=-. CTL model-checking has been used for proving the correctness of concurrent systems such as circuits and communication protocols. Our approach is to augment both the state-transition graph and logica... |

431 |
Automata for modeling real-time systems
- Alur, Dill
- 1990
(Show Context)
Citation Context ...nds with transitions. Examples of these are timed transition systems [32, 20], timed I/O automata [29], and Modecharts [24]. Our definition of timed graphs is based on the formalism of timed automata =-=[14, 4]-=-. Timed automata accept timed traces --- sequences of events in which each element has an associated real-valued time of occurrence. The semantics of timed automata is linear-time and event-based, whe... |

254 | A really temporal logic
- Alur, Henzinger
- 1989
(Show Context)
Citation Context ...duces a special tick transition in the model. Here time is viewed as a global state variable that ranges over the domain of natural numbers, and is incremented by one with every tick transition (e.g. =-=[32, 6, 10, 19]-=- ). This model allows arbitrarily many transitions of any process between two successive tick transitions. (The discrete-time model can be viewed as a special case where the events happen only in lock... |

231 |
Timing assumptions and verification of finite-state concurrent systems. In: Workshop Automatic Verification Methods for Finite-State Systems
- Dill
- 1989
(Show Context)
Citation Context ...uirements on the delays such as "the delay between two transitions equals 2 seconds." The third approach to modeling real-time behavior models time, more realistically, as a continuous quant=-=ity (e.g. [25, 29, 27, 14]-=-). We prefer to use this dense-time model (see [2] for some advantages of the dense-time model over the discrete models). With each transition we associate a time value chosen from the set of nonnegat... |

215 | The benefits of relaxing punctuality
- Alur, Feder, et al.
- 1996
(Show Context)
Citation Context ...eal-time systems modeled as timed graphs. We will briefly survey these results. Alur et.al. have developed an algorithm for checking specifications in the linear-time logic MITL against a timed graph =-=[5]-=-. The logic MITL extends the syntax of the lineartime temporal logic PTL by allowing subscripts on the temporal operators. The subscript on a temporal operator may be any nonsingular interval of R wit... |

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

94 |
Symbolic model checking: states and beyond
- Burch, Clarke, et al.
- 1992
(Show Context)
Citation Context ...ays to cope with the PSPACE complexity of the problem. Recently heuristics to implement CTL model-checking without explicitly enumerating all the states have been proposed. For instance, Burch et.al. =-=[11]-=- propose the use of binary decision diagrams to represent large state sets symbolically. Henzinger et.al. [21] have shown how to extend these symbolic methods to model-checking of TCTL formulas. Ackno... |

90 |
Techniques for automatic verification of real-time systems
- Alur
- 1991
(Show Context)
Citation Context ...ons equals 2 seconds." The third approach to modeling real-time behavior models time, more realistically, as a continuous quantity (e.g. [25, 29, 27, 14]). We prefer to use this dense-time model =-=(see [2]-=- for some advantages of the dense-time model over the discrete models). With each transition we associate a time value chosen from the set of nonnegative reals R. We regard computations as continuous ... |

87 | D.: Model-checking for Probabilistic Real-time Systems
- Alur, Courcoubetis, et al.
(Show Context)
Citation Context ...ng the semantics of TCTL-formulas 29 in this probabilistic model, the existential quantifier is interpreted as "with positive probability," and the universal quantifier means "with prob=-=ability 1." In [3]-=-, we present an algorithm for checking whether a GSMP satisfies its TCTLspecification. That algorithm combines model-checking algorithm of this paper with model-checking for discrete-time Markov chain... |

65 |
Minimum and maximum delay problems in real-time systems
- Courcoubetis, Yannakakis
- 1992
(Show Context)
Citation Context ... that is, operators such as 3 =3 , makes the model-checking problem undecidable! Courcoubetis and Yannakakis use timed graphs to solve certain minimum and maximum delay problems for real-time systems =-=[13]-=-. For instance, they show how to compute the earliest and the latest time a target state can appear along the runs of a timed graph given an initial state and a clock assignment. The research on timed... |

25 |
Proving Real-time Properties of Programs with Temporal Logic
- Bernstein, Harter
- 1981
(Show Context)
Citation Context ...here have been several temporal logics with quantitative time (see [7] for a survey). These include linear-time logics with discrete semantics [23, 32, 6, 19], linear-time logics with dense semantics =-=[8, 25]-=-, and branching-time logics with discrete semantics [18]. The syntax of our logic is very similar to that of Real-Time CTL of [18]. Verification algorithms have been developed for the logics with disc... |

16 |
Advances in Asynchronous Circuit Theory: Part I: Gate and Unbounded Intertial Delay Models
- Brzozowski, Seger
- 1990
(Show Context)
Citation Context ....g. bugs) will be overlooked. For instance, Brzozowski et.al. show that the reachability problem for asynchronous circuits with bounded delays cannot be solved correctly using the discrete-time model =-=[9]. Also the-=- choice of a sufficiently small time quantum to be "reasonably" safe may blow up the state space to the point where verification is no longer feasible. The fictitious-clock approach introduc... |

6 |
Modelling elapsed time in protocol specification
- Aggarwal, Kurshan
- 1983
(Show Context)
Citation Context ...e time explicitly in the underlying formal semantics for processes. There are three basic approaches to modeling real-time systems. Discrete-time models use the domain of integers to model time (e.g. =-=[1, 23, 18]-=-). This approach accurately describes the behavior of synchronous systems, where all components are driven by a common global clock. However, to model asynchronous systems it becomes necessary to disc... |

3 |
Combining CTL, trace theory and timing models. In Automatic Verification Methods for Finite State Systems
- Burch
- 1989
(Show Context)
Citation Context ...duces a special tick transition in the model. Here time is viewed as a global state variable that ranges over the domain of natural numbers, and is incremented by one with every tick transition (e.g. =-=[32, 6, 10, 19]-=- ). This model allows arbitrarily many transitions of any process between two successive tick transitions. (The discrete-time model can be viewed as a special case where the events happen only in lock... |