## Fischer's Protocol in Timed Process Algebra (1994)

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Citations: | 8 - 2 self |

### BibTeX

@MISC{Vereijken94fischer'sprotocol,

author = {Jan Joris Vereijken},

title = {Fischer's Protocol in Timed Process Algebra},

year = {1994}

}

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### Abstract

Timed algebraic process theories can be developed with quite different purposes in mind. One can aim for theoretical results about the theory itself (completeness, expressiveness, decidability), or one can aim for practical applicability to non-trivial protocols. Unfortunately, these aims do not go well together. In this paper we take two theories, which are probably of the first kind, and try to find out how well suited they are for practical verifications. We verify Fischer's protocol for mutual exclusion in the settings of discrete-time process algebra (ACP dt ) and real-time process algebra (ACP ur ). We do this by transforming the recursive specification into an equivalent linear specification, and then dividing out the maximal bisimulation relation. The required mutual exclusion result can then be found by reasoning about the obtained process graph. Finally, we consider the ease of the verification, and ways to adapt the theory to make it more practical. It will turn out that the...

### Citations

3387 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ........................... 23 Acknowledgments 36 Bibliography 36 1 Introduction In the past decade a lot of research has been done on algebraic process theories, the three most prominent ones being CCS =-=[Mil89]-=-, CSP [Hoa85], and ACP [BW90]. Although these theories are well established in their untimed version, there is no consensus regarding versions of CCS, CSP, and ACP extended with time. Admitted, there ... |

301 |
Solution to a problem in concurrent programming control
- Dijkstra
- 1965
(Show Context)
Citation Context ...nd each paper about mutual exclusion seems to have its own favorite subset of which ones to prove. In the case of Fischer’s protocol we choose, mostly following the earliest paper on mutual exclusio=-=n [Dij65], to p-=-rove the following three properties: • Actual mutual exclusion between the two critical sections, • Symmetry between the two components, • No starvation. We will not try to formalize these prope... |

229 | A fast mutual exclusion algorithm - Lamport - 1987 |

223 | A new solution of Dijkstra’s concurrent programming problem - Lamport - 1974 |

213 | An old-fashioned recipe for real time - Abadi, Lamport - 1994 |

158 | Real Time Process Algebra
- Baeten, Bergstra
- 1991
(Show Context)
Citation Context ...is done in a setting of dense time, using the theory ACPur. This theory was devised by Klusener [Klu93], and is closely related to ACPρ, the standard real-time extension of ACP by Baeten and Bergstra=-= [BB91]. 2sTh-=-e whole point of this exercise lies in the following two questions. First, “How well suited are the current timed extensions of ACP to verify real-life systems?”, and secondly, “With real-life v... |

40 | Additional comments on a problem in concurrent programming control - Knuth - 1966 |

28 | Putting time into proof outlines
- Schneider, Bloom, et al.
- 1992
(Show Context)
Citation Context ...This however does not mean too much; it is an almost trivial protocol, 16 E2sthat has been solved time and time again using all kinds of formalisms. But it is not all that bad either; see for example =-=[SBM92] w-=-here an (incomplete) proof is given of Fischer’s protocol. When it would be written out in full detail, that proof would be about as long and tedious as ours is [Sch94], and the same probably holds ... |

24 | Delayed choice: an operator for joining Message Sequence Charts
- Baeten, Mauw
- 1995
(Show Context)
Citation Context ...ly from those internal moments of choice we really want to abstract from. This could be implemented by introducing a special choice operator next to the ordinary +. For example, the delayed choice of =-=[BM94] or-=- a τ-angelic choice. • Secondly, it might be profitable to augment process algebra with a (limited) form of temporal logic. Looking at the linearization process of FPur in Appendix B, it is clear t... |

20 |
Models and Axioms for a Fragment of Real Time Process Algebra
- Klusener
- 1993
(Show Context)
Citation Context ... discrete time, using the theory ACPdt devised by Baeten and Bergstra [BB92a]. Secondly, a verification is done in a setting of dense time, using the theory ACPur. This theory was devised by Klusener =-=[Klu93], a-=-nd is closely related to ACPρ, the standard real-time extension of ACP by Baeten and Bergstra [BB91]. 2sThe whole point of this exercise lies in the following two questions. First, “How well suited... |

12 | Process Algebra and Structured Operational Semantics - Groote - 1991 |

10 | Additional comments on a problem in concurrent programming and control - deBruijn - 1967 |

9 | Layering of real-time distributed processes - Janssen, Poel, et al. - 1994 |

5 | Frame-based process logics
- Bergstra, Ponse
- 1995
(Show Context)
Citation Context ...noting the precise flow of time. When working with a hybrid process algebra-temporal logic theory (still predominantly algebraic!), these complications would probably not have arisen. See for example =-=[BBB93], -=-where this approach is investigated. • Thirdly, we might just as well admit that real-time verifications are difficult, and probably will remain so for some years to come. Therefore, it may be advis... |

5 | editors. RealTime: Theory - Bakker, Huizing, et al. - 1992 |

1 |
Re: where are you? Electronic mail message from Michael Fischer to Leslie Lamport. Arpanet message sent
- Fischer
- 1985
(Show Context)
Citation Context ...mal description of the protocol is given, together with an informal correctness argument. 2.1 History of the protocol The protocol we examine is a mutual exclusion protocol, first proposed by Fischer =-=[Fis85]-=-, and later studied in [Lam87, SBM92, AL92a, JPXZ94]. None of these studies uses process algebra to prove correctness, they all rely on some form of temporal logic or Floyd-Hoare logic. Instead of usi... |

1 |
The ABP and the CABP---a comparison of performances in real time process algebra
- Hillebrand
- 1994
(Show Context)
Citation Context ...theoretical results. As a consequence, a lot of papers have been published regarding completeness results, expressivity results, decidability results, and so on, but almost no paper (one exception is =-=[Hil94]) -=-gives an actual verification of a real system, not even a toy system. In this paper we will present such a more-or-less real system, namely Fischer’s protocol for mutual exclusion [Fis85, Lam87]. We... |

1 |
Proving mutual exclusion with process algebra
- Nieuwland
- 1990
(Show Context)
Citation Context ...3: Fischer’s protocol in discrete time (ACPdt). s(x ≔ i). If it wants to check if x has the value i, itperformstheactionr(x = i). (The idea to construct the variable server in this way was taken f=-=rom [Nie90].) The -=-process A is constructed as follows. First (in state A0) it waits for an undetermined amount of time till x is 0 (⌊r(x = 0)⌋ ω ). Then (in state A1)itsetsx to 1 (s(x ≔ 1)). After that (in state... |

1 | Vlijmen, editors. ACP94, workshop on algebra of communicating processes - Ponse, Verhoef, et al. - 1994 |

1 |
Personal communication. Typeset by L A T
- Schneider
- 1994
(Show Context)
Citation Context ...t bad either; see for example [SBM92] where an (incomplete) proof is given of Fischer’s protocol. When it would be written out in full detail, that proof would be about as long and tedious as ours i=-=s [Sch94]-=-, and the same probably holds for a detailed temporal logic proof [Aba94]. Looking at our proof one observes that, although conceptually very clear and easy, the inner workings required a lot of bothe... |