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On the invariants of coloured Petri Nets

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Advances in Petri Nets 1985 (APN 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 222))

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Abstract

In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in the analysis of concurrent systems.

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References

  1. T. Agerwala and Y.C. Amphai, ‘A Synthesis Rule for Concurrent Systems', Proceedings of IEEE Conference on Design Automation, 1978, pp. 305–311.

    Google Scholar 

  2. H.J. Genrich and K. Lautenbach, ‘The Analysis of distributed systems by predicate/transition nets', Semantics of Concurrent Computation, Evian 1979, G. Kahn (ed.), Lecture Notes in Computer Science, Vol.70, Springer verlag 1979, pp. 123–146.

    Google Scholar 

  3. H.J. Genrich and K. Lautenbach, ‘System Modelling with High-Level Petri Nets', Theoretical Computer Science, Vol.13, 1981, pp. 109–136, North-Holland Publishing Company.

    Article  Google Scholar 

  4. M. Jantzen and R. Valk, ‘Formal Properties of Place/Transition Nets', Net Theory and Applications, Hamburg 1979, W. Brauer (ed.), Lecture Notes in Computer Science, Vol.84, Springer-Verlag 1980, pp. 165–212.

    Google Scholar 

  5. K. Jensen, ‘Coloured Petri Nets and the Invariant Method', Theoretical Computer Science, Vol.14, 1981, pp. 317–336, North-Holland Publishing Company.

    Article  Google Scholar 

  6. K. Jensen, ‘How to find Invariants for Coloured Petri Nets', Mathematical Foundations of Computer Science, 1981, J. Gruska and M. Chytil (eds.), Lecture Notes in Computer Science, Vol.118, Springer-Verlag 1981, pp. 327–338.

    Google Scholar 

  7. G. Memmi and G. Roucairol, ‘Linear Algebra in Net Theory', Net Theory and Applications, Hamburg 1979, W. Brauer (ed.), Lecture Notes in Computer Science, Vol.84, Springer-Verlag 1980, pp. 213–224.

    Google Scholar 

  8. Y. Narahari and N. Viswanadham, ‘A Petri Net Approach to the modelling and analysis of Flexible manufacturing systems', To appear in: Annals of Operations Research, Vol.3, 1986.

    Google Scholar 

  9. J.L. Peterson, ‘Petri Nets', ACM Computing Surveys, Vol.9, No.3, September 1977, pp. 223–252.

    Article  Google Scholar 

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G. Rozenberg

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© 1986 Springer-Verlag Berlin Heidelberg

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Narahari, Y., Viswanadham, N. (1986). On the invariants of coloured Petri Nets. In: Rozenberg, G. (eds) Advances in Petri Nets 1985. APN 1985. Lecture Notes in Computer Science, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016219

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  • DOI: https://doi.org/10.1007/BFb0016219

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16480-7

  • Online ISBN: 978-3-540-39822-6

  • eBook Packages: Springer Book Archive

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