## The Observational Power of Clocks (1994)

Citations: | 39 - 4 self |

### BibTeX

@INPROCEEDINGS{Alur94theobservational,

author = {Rajeev Alur and Costas Courcoubetis and Thomas A. Henzinger},

title = {The Observational Power of Clocks},

booktitle = {},

year = {1994},

pages = {162--177},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

We develop a theory of equivalences for timed systems. Two systems are equivalent iff external observers cannot observe differences in their behavior. The notion of equivalence depends, therefore, on the distinguishing power of the observers. The power of an observer to measure time results in untimed, clock, and timed equivalences: an untimed observer cannot measure the time difference between events; a clock observer uses a clock to measure time differences with finite precision; a timed observer is able to measure time differences with arbitrary precision. We show that the distinguishing power of clock observers grows with the number of observers, and approaches, in the limit, the distinguishing power of a timed observer. More precisely, given any equivalence for untimed systems, two timed systems are k-clock congruent, for a nonnegative integer k, iff their compositions with every environment that uses k clocks are untimed equivalent. Both k-clock bisimulation congruence and k-cloc...

### Citations

1989 | A theory of timed automata
- Alur, Dill
- 1994
(Show Context)
Citation Context ... different capabilities of an observer to measure time. A timed system always proceeds in one of two ways---by performing an action or by letting a certain amount of real time pass (see, for example, =-=[4, 8, 12, 16]-=-). The observability of actions and time delays are orthogonal issues, and as we are interested in the latter, we settle the former by studying the common untimed equivalences of bisimilarity (Section... |

477 | Symbolic model checking for real-time systems
- Henzinger, Nicollin, et al.
- 1992
(Show Context)
Citation Context ...of the clock values with integer constants and reset some of the clocks. This model of timed automata has been widely and successfully used for the specification and verification of real-time systems =-=[1, 3, 4, 6, 7, 9, 11, 12]-=-. Our results on bisimulation equivalences in Section 3 are obtained by studying bisimulation games. We define time-abstract (or untimed), k-clock, and timed bisimulation games. Suppose that Player I ... |

240 | A really temporal logic
- Alur, Henzinger
- 1994
(Show Context)
Citation Context ...ms in the trace model, provided the number of environment clocks is bounded. Linear-time logics with clocks If we extend linear temporal logic with clock variables, we obtain the real-time logic TPTL =-=[5]-=-. Since we consider only finite words, we omit the temporal operator 2. The formulas of TPTL ffi are defined inductively as OE ::= xsc j csx j :OE j OE 1sOE 2 j floe: OE j (x := 0): OE for clocks x, n... |

98 | Parametric real-time reasoning
- Alur, Henzinger, et al.
- 1993
(Show Context)
Citation Context ...of the clock values with integer constants and reset some of the clocks. This model of timed automata has been widely and successfully used for the specification and verification of real-time systems =-=[1, 3, 4, 6, 7, 9, 11, 12]-=-. Our results on bisimulation equivalences in Section 3 are obtained by studying bisimulation games. We define time-abstract (or untimed), k-clock, and timed bisimulation games. Suppose that Player I ... |

83 |
Model checking in dense real time
- Alur, Courcoubetis, et al.
- 1993
(Show Context)
Citation Context ...of the clock values with integer constants and reset some of the clocks. This model of timed automata has been widely and successfully used for the specification and verification of real-time systems =-=[1, 3, 4, 6, 7, 9, 11, 12]-=-. Our results on bisimulation equivalences in Section 3 are obtained by studying bisimulation games. We define time-abstract (or untimed), k-clock, and timed bisimulation games. Suppose that Player I ... |

80 | From ATP to Timed Graphs and Hybrid Systems
- Nicollin, Yovine
- 1991
(Show Context)
Citation Context ... different capabilities of an observer to measure time. A timed system always proceeds in one of two ways---by performing an action or by letting a certain amount of real time pass (see, for example, =-=[4, 8, 12, 16]-=-). The observability of actions and time delays are orthogonal issues, and as we are interested in the latter, we settle the former by studying the common untimed equivalences of bisimilarity (Section... |

77 | Minimization of timed transition systems - Alur, Courcoubetis, et al. - 1992 |

64 |
Decidability of bisimulation equivalences for parallel timer processes
- Čerāns
- 1993
(Show Context)
Citation Context ...stinguishing power of an environment increases with the number of environment processes. Decision procedures are known for time-abstract and timed bisimilarity and for time-abstract trace equivalence =-=[2, 4, 14, 15, 17]-=-. We present algorithms for deciding the k-clock congruences. In the bisimulation world, where the k-clock hierarchy collapses at 2n + 1 clocks for a given pair of systems with n clocks, we obtain a n... |

63 |
Minimum and maximum delay problems in real-time systems
- Courcoubetis, Yannakakis
- 1992
(Show Context)
Citation Context |

63 | Temporal proof methodologies for real-time systems
- Henzinger, Manna, et al.
- 1990
(Show Context)
Citation Context ... different capabilities of an observer to measure time. A timed system always proceeds in one of two ways---by performing an action or by letting a certain amount of real time pass (see, for example, =-=[4, 8, 12, 16]-=-). The observability of actions and time delays are orthogonal issues, and as we are interested in the latter, we settle the former by studying the common untimed equivalences of bisimilarity (Section... |

57 |
R.J.H.: Comparative concurrency semantics and refinement of actions
- Glabbeek
- 1996
(Show Context)
Citation Context ...arity and trace equivalence---and although there may be no agreement as to which equivalence is most appropriate, the relationship between different equivalences is well understood (see, for example, =-=[13]-=-). This is not the case for timed systems, where the introduction of time as a continuous quantity makes the question of what is observable even more subtle. This paper studies the relationship betwee... |

40 | Action transducers and timed automata
- Lynch, Vaandrager
- 1992
(Show Context)
Citation Context ...games, and logics Clocks provide a clean and general paradigm for specifying timed systems: clocks have been added to such diverse languages as temporal logic [5], !-automata [4], and process algebra =-=[11]-=-. We develop our results using the model of timed automata (Section 2). A timed automaton operates with finite control---a finite set of control locations and a finite set of real-valued clocks. All c... |

39 | Computing accumulated delays in real-time systems
- Alur, Courcoubetis, et al.
(Show Context)
Citation Context |

39 | Time-abstracted bisimulation: Implicit specifications and decidability
- Larsen, Yi
- 1997
(Show Context)
Citation Context ...responding timed equivalence on initial system states, in which all clock values are 0. Related work The relationship between timed bisimilarity and untimed bisimulation congruence is studied also in =-=[10]-=-. There, it is shown that timed bisimilarity coincides with untimed bisimulation congruence provided that the observer can compare clock values with arbitrary rational constants; indeed, in this scena... |

36 |
An efficient algorithm for minimizing real-time transition systems. Formal Methods in System Design, 11(2):113–136
- Yannakakis, Lee
- 1997
(Show Context)
Citation Context ...stinguishing power of an environment increases with the number of environment processes. Decision procedures are known for time-abstract and timed bisimilarity and for time-abstract trace equivalence =-=[2, 4, 14, 15, 17]-=-. We present algorithms for deciding the k-clock congruences. In the bisimulation world, where the k-clock hierarchy collapses at 2n + 1 clocks for a given pair of systems with n clocks, we obtain a n... |

24 | K.G.: Timed modal specification - theory and tools
- Čerāns, Godskesen, et al.
- 1993
(Show Context)
Citation Context ...stinguishing power of an environment increases with the number of environment processes. Decision procedures are known for time-abstract and timed bisimilarity and for time-abstract trace equivalence =-=[2, 4, 14, 15, 17]-=-. We present algorithms for deciding the k-clock congruences. In the bisimulation world, where the k-clock hierarchy collapses at 2n + 1 clocks for a given pair of systems with n clocks, we obtain a n... |

6 | Comparative Concurrency Semantics and Re nement of Actions - Glabbeek - 1990 |

4 |
Real-time behavior of asynchronous agents
- Wang
- 1990
(Show Context)
Citation Context |

3 | K.G.: Timed modal speci cation - theory and tools - Cerans, Godskesen, et al. - 1993 |