Advances in Petri Nets 1984 pp 32-47 | Cite as
Concurrency axioms and D-continuous posets
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Abstract
A non-sequential process can be modelled by a partially ordered set of basic occurrences. Conversely, one is led to study the properties to be fulfilled by a poset so that it can reasonably be viewed as the model of a non-sequential process. To this end, Petri has proposed a set of concurrency axioms which include D-continuity, a generalised version of Dedekind's completeness property of the reals.
In this paper we give some general characterisations of D-continuous posets. We also study the relationship between D-continuity and the remaining concurrency axioms of Petri.
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References
- 1.E. Best: A Theorem on the Characteristics of Non-sequential Processes. Fundamental Informaticae Vol. 3(1), 77–94 (1980).Google Scholar
- 2.E.Best: Concurrent Behaviour: Sequences, Processes and Axioms. Arbeitspapiere der GMD No.118 (1984), also in Proc. of CMU Workshop on Concurrency (1984).Google Scholar
- 3.E.Best and A.Merceron: Some Properties of Non-sequential Processes. GMD-ISF Report 82.07 (1982).Google Scholar
- 4.E. Best and A. Merceron: Discreteness, K-density and D-continuity of Occurrence Nets. Lecture Notes in Computer Science, Springer Verlag Vol.145, 73–83 (1982).Google Scholar
- 5.E. Best and A. Merceron: Concurrency Axioms and D-continuous Posets. 4th Petri Net Workshop, Toulouse (1983).Google Scholar
- 6.E.Best and A.Merceron: Frozen Tokens and D-continuity: A Study in Relating System Properties to Process Properties. In this Volume.Google Scholar
- 7.E. Best and B. Randell: A Formal Model of Atomicity in Asynchronous Systems. Acta Informatica Vol.16, 93–124 (1981).CrossRefGoogle Scholar
- 8.C.Fernández, M.Nielsen and P.S.Thiagarajan: A Note on Observable Observable Occurrence Nets. 5th Petri Net Workshop, Århus (1984). Also to appear in this Volume.Google Scholar
- 9.C. Fernández and P.S. Thiagarajan: D-Continuous Causal Nets: A Model of Non-sequential Processes. TCS Vol.28, 171–196 (1984).CrossRefGoogle Scholar
- 10.C.Fernández and P.S.Thiagarajan: A Note D-continuous Causal Nets. 3rd Petri Net Workshop, Varenna (1982).Google Scholar
- 11.H.J. Genrich and P.S. Thiagarajan: A Theory of Bipolar Synchronisation Schemes. TCS Vol.30, 241–318 (1984).Google Scholar
- 12.H.J. Genrich and E. Stankiewicz-Wiechno: A Dictionary of some Basic Notions of Net Theory. Lecture Notes in Computer Science, Springer Verlag Vol.84, 519–535 (1980).Google Scholar
- 13.W.M.Lu and A.Merceron: The Equivalence between the Well Behaved Bipolar Schemes and the Live and Safe Free Choice Nets without Frozen Tokens. 5th Petri Net Workshop, Århus (1984).Google Scholar
- 14.M. Nielsen, G. Plotkin and G. Winskel: Petri Nets, Event Structures and Domains. TCS Vol.13, 85–108 (1981).Google Scholar
- 15.C.A.Petri: Non-Sequential Processes. GMD-ISF Report 77.05 (1977).Google Scholar
- 16.C.A. Petri: Concurrency. Lecture Notes in Computer Science, Springer Verlag Vol.84, 251–260 (1980).Google Scholar
- 17.C.A. Petri: State Transition Structures in Physics and in Computation. International Journal on Theoretical Physics, Vol.21(12), 979–992 (1982).Google Scholar
- 18.H.Plünnecke: Schnitte in Halbordnungen. GMD-ISF Report 81.09 (1981). Shorter version also to appear in this Volume.Google Scholar
- 19.H.Plünnecke: Partial Orders. Arbeitspapiere der GMD No.93 (1984).Google Scholar
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