## Superposition Refinement of Reactive Systems (1993)

Venue: | FORMAL ASPECTS OF COMPUTING |

Citations: | 37 - 8 self |

### BibTeX

@ARTICLE{Back93superpositionrefinement,

author = {R. J. R. Back and K. Sere},

title = {Superposition Refinement of Reactive Systems},

journal = {FORMAL ASPECTS OF COMPUTING},

year = {1993},

volume = {8},

pages = {324--346}

}

### Years of Citing Articles

### OpenURL

### Abstract

Superposition refinement enhances an algorithm by superposing one computation mechanism onto another mechanism, in a way that preserves the behavior of the original mechanism. Superposition seems to be particularly well suited to the development of parallel and distributed programs: an originally simple sequential algorithm can be extended with mechanisms that distribute control and state information to many processes, thus permitting efficient parallel execution of the algorithm. We will in this paper show how superposition of reactive systems is expressed in the refinement calculus. We illustrate the power of this method by a case study, showing how a distributed broadcasting system is derived through a sequence of superposition refinements.

### Citations

1543 |
A Discipline of Programming
- Dijkstra
- 1976
(Show Context)
Citation Context ...w how to describe superposition of action systems within this calculus. Refinement calculus is a formalization of the stepwise refinement method based on the weakest precondition calculus of Dijkstra =-=[11]-=-. It was proposed by Back [1, 2] and has later been further elaborated by several researchers [8, 16, 17]. A combination of the refinement calculus and the action system formalism have turned out to p... |

778 |
Parallel Program Design: A Foundation
- Chandy, Misra
- 1988
(Show Context)
Citation Context ...time. Superposition as a method for program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. [12], Back and Kurki-Suonio et al. [4, 15], Chandy and Misra =-=[10]-=-, Francez et al. [9, 13], Katz [14] and others. In this paper we will study superposition of parallel and distributed programs, within the action system framework. This formalism was introduced by Bac... |

220 |
On-the-fly garbage collection: an exercise in cooperation
- Dijkstra, Lamport, et al.
- 1978
(Show Context)
Citation Context ...le a number of interrelated design questions all at the same time. Superposition as a method for program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. =-=[12]-=-, Back and Kurki-Suonio et al. [4, 15], Chandy and Misra [10], Francez et al. [9, 13], Katz [14] and others. In this paper we will study superposition of parallel and distributed programs, within the ... |

163 |
A Theoretical Basis for Stepwise Refinement and the Programming Calculus
- Morris
- 1987
(Show Context)
Citation Context ...ormalization of the stepwise refinement method based on the weakest precondition calculus of Dijkstra [11]. It was proposed by Back [1, 2] and has later been further elaborated by several researchers =-=[8, 16, 17]-=-. A combination of the refinement calculus and the action system formalism have turned out to provide an uniform foundation for the derivation of parallel algorithms by stepwise refinement [6, 19]. In... |

154 |
A calculus of refinements for program derivations
- Back
- 1988
(Show Context)
Citation Context ...n of action systems within this calculus. Refinement calculus is a formalization of the stepwise refinement method based on the weakest precondition calculus of Dijkstra [11]. It was proposed by Back =-=[1, 2]-=- and has later been further elaborated by several researchers [8, 16, 17]. A combination of the refinement calculus and the action system formalism have turned out to provide an uniform foundation for... |

140 |
The Specification Statement
- Morgan
- 1988
(Show Context)
Citation Context ...ormalization of the stepwise refinement method based on the weakest precondition calculus of Dijkstra [11]. It was proposed by Back [1, 2] and has later been further elaborated by several researchers =-=[8, 16, 17]-=-. A combination of the refinement calculus and the action system formalism have turned out to provide an uniform foundation for the derivation of parallel algorithms by stepwise refinement [6, 19]. In... |

139 |
Decentralization of process nets with centralized control
- Back, Kurki-Suonio
- 1989
(Show Context)
Citation Context ...questions all at the same time. Superposition as a method for program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. [12], Back and Kurki-Suonio et al. =-=[4, 15]-=-, Chandy and Misra [10], Francez et al. [9, 13], Katz [14] and others. In this paper we will study superposition of parallel and distributed programs, within the action system framework. This formalis... |

122 |
A superimposition control construct for distributed systems
- Katz
- 1993
(Show Context)
Citation Context ... program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. [12], Back and Kurki-Suonio et al. [4, 15], Chandy and Misra [10], Francez et al. [9, 13], Katz =-=[14]-=- and others. In this paper we will study superposition of parallel and distributed programs, within the action system framework. This formalism was introduced by Back and Kurki-Suonio in [4], together... |

119 |
Re Calculus, Part II: Parallel and Reactive Programs
- Back
- 1990
(Show Context)
Citation Context ... refinement [6, 19]. In parallel algoritms the notion of correctness we want to preserve is total correctness. The refinement calculus has been extended to stepwise refinement of reactive programssin =-=[3]-=-. In these systems the externally observable behaviour of a program must be preserved in every refinement step. Superposition refinement of reactive systems is a special case of the general method for... |

110 |
Correctness Preserving Program Refinements: Proof Theory and Applications, volume 131
- Back
- 1980
(Show Context)
Citation Context ...n of action systems within this calculus. Refinement calculus is a formalization of the stepwise refinement method based on the weakest precondition calculus of Dijkstra [11]. It was proposed by Back =-=[1, 2]-=- and has later been further elaborated by several researchers [8, 16, 17]. A combination of the refinement calculus and the action system formalism have turned out to provide an uniform foundation for... |

61 |
Stepwise refinement of parallel algorithms
- Back, Sere
- 1990
(Show Context)
Citation Context ...[8, 16, 17]. A combination of the refinement calculus and the action system formalism have turned out to provide an uniform foundation for the derivation of parallel algorithms by stepwise refinement =-=[6, 19]-=-. In parallel algoritms the notion of correctness we want to preserve is total correctness. The refinement calculus has been extended to stepwise refinement of reactive programssin [3]. In these syste... |

59 | Re Calculus, Part I: Sequential Nondeterministic Programs
- Back, Wright
- 1990
(Show Context)
Citation Context ...ormalization of the stepwise refinement method based on the weakest precondition calculus of Dijkstra [11]. It was proposed by Back [1, 2] and has later been further elaborated by several researchers =-=[8, 16, 17]-=-. A combination of the refinement calculus and the action system formalism have turned out to provide an uniform foundation for the derivation of parallel algorithms by stepwise refinement [6, 19]. In... |

50 |
Radiative processes
- Randall, Forman, et al.
- 1979
(Show Context)
Citation Context ...s a method for program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. [12], Back and Kurki-Suonio et al. [4, 15], Chandy and Misra [10], Francez et al. =-=[9, 13]-=-, Katz [14] and others. In this paper we will study superposition of parallel and distributed programs, within the action system framework. This formalism was introduced by Back and Kurki-Suonio in [4... |

14 | Action System Approach to the Specification and Design of Distributed Systems
- Kurki-Suonio, Järvinen
(Show Context)
Citation Context ...questions all at the same time. Superposition as a method for program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. [12], Back and Kurki-Suonio et al. =-=[4, 15]-=-, Chandy and Misra [10], Francez et al. [9, 13], Katz [14] and others. In this paper we will study superposition of parallel and distributed programs, within the action system framework. This formalis... |

12 |
Stepwise Derivation of Parallel Algorithms
- Sere
- 1990
(Show Context)
Citation Context ...erms of the events or actions which processes in the system carry out in co-operating with each other. Action systems support the construction of parallel and distributed systems in a stepwise manner =-=[4, 19]-=-. Stepwise refinement of action systems starts with a specification of the intended behavior of the system, given as a sequential statement. The goal is to construct an action system that satisfies ce... |

8 |
Deriving an occam implementation of action systems
- Back, Sere
- 1990
(Show Context)
Citation Context ...ion of the intended behavior of the system, given as a sequential statement. The goal is to construct an action system that satisfies certain criteria and fits into some predefined syntactic category =-=[4, 5]-=- for which an efficient implementation on the assumed distributed architecture can be given. Superposition refinements of action systems are done in order to increase the degree of parallelism of the ... |

7 |
A methodology for developing distributed programs
- Ramesh, Mehndiratta
- 1987
(Show Context)
Citation Context ...positioning. Action systems have similarities with other event-based formalisms like UNITY of Chandy and Misra [10], interacting processes of Francez [13] and shared actions of Ramesh and Mehndiratta =-=[18]-=- among others. The system behavior is in these formalisms described in terms of the events or actions which processes in the system carry out in co-operating with each other. Action systems support th... |

5 |
A compositional approach to superposition
- Bougé
- 1988
(Show Context)
Citation Context ...s a method for program refinement has come up in a number of different contexts, e.g. in the works of Dijkstra et al. [12], Back and Kurki-Suonio et al. [4, 15], Chandy and Misra [10], Francez et al. =-=[9, 13]-=-, Katz [14] and others. In this paper we will study superposition of parallel and distributed programs, within the action system framework. This formalism was introduced by Back and Kurki-Suonio in [4... |

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