## Metric spaces as models for real-time concurrency (1987)

Citations: | 42 - 3 self |

### BibTeX

@INPROCEEDINGS{Reed87metricspaces,

author = {G. M. Reed and A. W. Roscoe},

title = {Metric spaces as models for real-time concurrency},

booktitle = {},

year = {1987},

pages = {331--343},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. We propose a denotational model for real time concurrent systems, based on the failures model for CSP. The fixed point theory is based on the Banach fixed point theorem for complete metric spaces, since the introduction of time as a measure makes all recursive operators naturally contractive. This frees us from many of the constraints imposed by partial orders on the treatment of nondeterminism and divergence. 1

### Citations

3400 | Communicating Sequential Processes - Hoare - 1985 |

156 | A timed model for communicating sequential processes
- Reed, Roscoe
- 1988
(Show Context)
Citation Context ...ntimed theory. We have chosen to base our work on (extensions of) the theoretical version of CSP and to try to discover models that have links with that language’s untimed theory. In an earlier paper =-=[RR]-=- we showed how the traces model [H1] could be expanded to include time. In this paper we give a timed version of the ‘failures’ model (including divergence) described in [BR,H2]. One of the main purpo... |

83 | Specification-oriented semantics for communicating pro-cesses. Acta Informatica 23 - Olderog, Hoare - 1986 |

66 |
An improved failures model for communicating processes
- Brookes, Roscoe
- 1985
(Show Context)
Citation Context ... order). By using a metric space we have been able to achieve the same effect more easily. 3.3 Infinite hiding The reader will note that the axiom of bounded nondeterminism from the failures model in =-=[BR]-=- is not included in our model: or, in a timed context, (∀Y ∈ p(X), (s, Y ) ∈ S) ⇒ (s, X) ∈ S I ∈ T INT ∧ X ∈ P (Σ) such that (∀Y ∈ p(X), ∃α such that (s, α, ℵ ∪ (I × Y )) ∈ S) ⇒ ∃α ′ such that (s, α ′... |

47 |
Refusal testing
- Phillips
- 1987
(Show Context)
Citation Context ...ter traces are no longer properly compositional. Other authors [J,Bo] have remarked on this and suggested or introduced similar solutions (based on partial orders rather than metric spaces). Phillips =-=[P]-=- has studied the corresponding untimed congruence. The reader may note that the traces of P \a depend in a crucial way on the (timed) failures of P . (This is clearly illustrated by the second example... |

16 | Infinite words, infinite trees, infinite computations - Nivat - 1979 |

13 |
A model for communicating sequential processes, On the construction uf programs CUP
- Hoare
- 1980
(Show Context)
Citation Context ...e our work on (extensions of) the theoretical version of CSP and to try to discover models that have links with that language’s untimed theory. In an earlier paper [RR] we showed how the traces model =-=[H1]-=- could be expanded to include time. In this paper we give a timed version of the ‘failures’ model (including divergence) described in [BR,H2]. One of the main purposes of this paper is to show how rea... |

10 | Rounds: Connection between two Theories of Concurrency: Metric Spaces and Synchronisation Trees - Golson, C - 1983 |

9 | Compositional semantics for real-time distributed computing - Koymans, Shyamasundar, et al. - 1985 |

6 | A theory of communicating sequential processes, Oxford University Computing Laboratory technical monograph PRG-16 - Hoare, Brookes, et al. - 1981 |

5 | A mathematical theory of communicating processes, Oxford University D.Phil thesis - Roscoe - 1982 |

4 | Applications of topology to the semantics of communicating processes - Rounds - 1985 |

2 | A timed model for communicating processes, Oxford University D.Phil thesis - Jones - 1982 |

1 | A time-based model for occam, Oxford University D.Phil. thesis - Boucher - 1986 |

1 |
Fixed point theory for communication and concurency
- Broy
- 1982
(Show Context)
Citation Context ...being forced to take this very strict view, and would have prefered a theory more like that of the timed model. This has lead them to use alternative fixed point theories such as optimal fixed points =-=[Broy]-=- (usually using more than one partial order). By using a metric space we have been able to achieve the same effect more easily. 3.3 Infinite hiding The reader will note that the axiom of bounded nonde... |