Abstract
We formally introduce arc-typed nets as a model for causality based specifications. The new feature of arc-typed nets is the distinction of different arc-types; the different arc-types carry over to a process of the net. Therefore, there are different types of causalities in a run of an arc-typed net.
Arc-typed nets have informally been used for modelling and verifying consistency protocols. It turned out that arc-typed nets provide an adequate level of abstraction for these kind of applications. We demonstrate the application of arc-typed nets by specifying, modelling, and verifying a simple consistency protocol.
Supported by the Deutsche Forschungs Gemeinschaft, Projects: Verteilte Algorithmen and SFB 342 TP YE1.
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J. K. Bennet, J.B. Carter, and W. Zwaenepoel. Munin: Distributed shared memory based on type-specific memory coherence. In 2nd ACM SIGPLAN Symposium on Principles and Practise of Parallel Programming. ACM March 1990.
Eike Best and César Fernández. Nonsequential Processes, EATCS Monographs on Theoretical Computer Science 13. Springer-Verlag, 1988.
Dominik Gomm and Ekkart Kindler. Causality based specification and correctness proof of a virtually shared memory scheme. SFB-Bericht 342/6/91 B, Technische Universität München, August 1991.
Dominik Gomm and Ekkart Kindler. A weakly coherent virtually shared memory scheme: Formal specification and analysis. SFB-Bericht 342/5/91 B, Technische Universität München, August 1991.
Dominik Gomm and Ekkart Kindler. Causality based proof of a distributed shared memory system. In A. Bode and M. Dal Cin, editors, Parallel Computer Architectures: Theory, Hardware, Software, Applications, LNCS 732, pages 131–149. Springer-Verlag, 1993.
Ursula Goltz and Wolfgang Reisig. The non-sequential behaviour of Petri nets. Information and Control, 57:125–147, 1983.
Jeremy Gunawardena. Geometric logic, causality and event structures. In J. Baeten and J. Groote, editors, CONCUR '91, LNCS 527, pages 266–280. Springer-Verlag, 1991.
Jeremy Gunawardena. Causal automata. Theoretical Computer Science, 101:265–288, 1992.
Kurt Jensen. Coloured Petri Nets, Volume 1: Basic Concepts. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1992.
Kurt Jensen. Coloured Petri Nets, Volume 2: Analysis Methods. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1995.
Joost-Pieter Katoen. Causal behaviours and nets. In Giorgio De Michelis and Michel Diaz, editors, Application and Theory of Petri Nets 1995, LNCS 935, pages 258–277. Springer-Verlag, June 1995.
Ekkart Kindler, Andreas Listl, and Rolf Walter. Kausalitätsbasierte Beweismethoden für parallele Datenbanksysteme: Eine Fallstudie. Informatik-Berichte 30, Humboldt-Universität zu Berlin, Institut für Informatik, June 1994.
Ekkart Kindler, Andreas Listl, and Rolf Walter. A specification method for transaction models with data replication. Informatik-Berichte 56, Humboldt-Universität zu Berlin, March 1996.
Leslie Lamport. Time, clocks, and the ordering of events in a distributed system. Communications of the ACM, 21(7):558–565, July 1978.
Wolfgang Reisig. Petri nets and algebraic specifications. Theoretical Computer Science, 80:1–34, May 1991.
Einar Smith and Wolfgang Reisig. The semantics of a net is a net, an exercise in general net theory. In K. Voss, H.J. Genrich, and G. Rozenberg, editors, Concurrency and Nets. Springer-Verlag, 1987.
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Kindler, E., Walter, R. (1996). Arc-typed Petri Nets. In: Billington, J., Reisig, W. (eds) Application and Theory of Petri Nets 1996. ICATPN 1996. Lecture Notes in Computer Science, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61363-3_16
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DOI: https://doi.org/10.1007/3-540-61363-3_16
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