Skip to main content

Two Algebraic Process Semantics for Contextual Nets

  • Chapter
  • First Online:
Unifying Petri Nets

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2128))

Abstract

We show that the so-called ‘Petri nets are monoids’ approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Baldan. Modelling concurrent computations: From contextual Petri nets to graph grammars. Ph.D. thesis, TD-1/00, Dipartimento di Informatica, Universitá di Pisa, 2000.

    Google Scholar 

  2. P. Baldan, A. Corradini, and U. Montanari. An event structure semantics for P/T contextual nets: Asymmetric event structures. In Proc. FoSSaCS’98, Foundations of Software Science and Computation Structures, (M. Nivat, Ed.), vol. 1378 of Lect. Notes in Comput. Sci., pp. 63–80. Springer, 1998.

    Google Scholar 

  3. E. Best and R. Devillers. Sequential and concurrent behaviour in Petri net theory. Theoretical Computer Science, 55:87–136, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Bruni. Tile Logic for Synchronized Rewriting of Concurrent Systems. Ph.D. thesis, TD-1/99, Dipartimento di Informatica, Universitá di Pisa, 1999.

    Google Scholar 

  5. R. Bruni, J. Meseguer, U. Montanari, and V. Sassone. A comparison of Petri net semantics under the collective token philosophy. In Proc. ASIAN’98, 4th Asian Computing Science Conference, (J. Hsiang, A. Ohori, Eds.), vol. 1538 of Lect. Notes in Comput. Sci., pp. 225–244. Springer, 1998.

    Google Scholar 

  6. R. Bruni, J. Meseguer, U. Montanari, and V. Sassone. Functorial semantics for Petri nets under the individual token philosophy. In Proc. CTCS’99, 8th conference on Category Theory and Computer Science, (M. Hofmann, G. Rosolini, D. Pavlovic, Eds.), vol. 29 of Elect. Notes in Comput. Sci., 19 pages. Elsevier Science, 1999.

    Google Scholar 

  7. R. Bruni and V. Sassone. Algebraic models for contextual nets. In ICALP2000, 27th Int. Coll. on Automata, Languages and Programming, (U. Montanari, J. Rolim, E. Welzl, Eds.), vol. 1853 of Lect. Notes in Comput. Sci., pp. 175–186. Springer, 2000.

    Google Scholar 

  8. N. Busi and M. Pinna. Non sequential semantics for contextual P/T nets. In Application and Theory of Petri Nets, vol. 1091 of Lect. Notes in Comput. Sci., pp. 113–132. Springer, 1996.

    Google Scholar 

  9. N. Busi. Petri nets with inhibitor and read arcs: Semantics, analysis and application to process calculi. Ph.D. thesis, TD-1/99, Dipartimento di Informatica, Universitá di Siena, 1998.

    Google Scholar 

  10. S. Christensen and N.D. Hansen. Coloured Petri nets extended with place capacities, test arcs and inhibitor arcs. In ICATPN’93, 14th Int. Conf. Applications and Theory of Petri Nets, (M.A. Marsan, Ed.), vol. 691 of Lect. Notes in Comput. Sci., pp. 186–205. Springer, 1993.

    Google Scholar 

  11. A. Corradini and U. Montanari. An algebraic semantics for structured transition systems and its application to logic programs. Theoretical Computer Science, 103:51–106, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  12. P. Degano, J. Meseguer, and U. Montanari. Axiomatizing net computations and processes. In Proc. LICS’89, 4th Symposium on Logic in Computer Science, pp. 175–185. IEEE Computer Society Press, 1989.

    Google Scholar 

  13. P. Degano, J. Meseguer, and U. Montanari. Axiomatizing the algebra of net computations and processes. Acta Inform., 33(7):641–667, 1996.

    Article  MathSciNet  Google Scholar 

  14. J. Desel, G. Juhás, and R. Lorenz. Process semantics of Petri nets over partial algebra. In Proc. ICATPN 2000, 21st Int. Conf. on Application and Theory of Petri Nets, (M. Nielsen, D. Simpson, Eds.), vol. 1825 of Lect. Notes in Comput. Sci., pp. 146–165. Springer, 2000.

    Google Scholar 

  15. H. Ehrig and J. Padberg. Uniform approach to Petri nets. In Proc. Foundations of Computer Science: Potential-Theory-Cognition, (C. Freska, M. Jantzen, R. Valk, Eds.), vol. 1337 of Lect. Notes in Comput. Sci., pp. 219–231. Springer, 1997.

    Google Scholar 

  16. F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proc. ICALP’98, 25th International Colloquium on Automata, Languages, and Programming, (K.G. Larsen, S. Skyum, G. Winskel, Eds.), vol. 1443 of Lect. Notes in Comput. Sci., pp. 296–308. Springer, 1998.

    Google Scholar 

  17. F. Gadducci and U. Montanari. The tile model. In Proof, Language and Interaction: Essays in Honour of Robin Milner, (G. Plotkin, C. Stirling, and M. Tofte, Eds.). MIT Press, 2000.

    Google Scholar 

  18. R.J. van Glabbeek and G.D. Plotkin. Configuration structures. In Proc. LICS’95, 10th Symposium on Logic in Computer Science, pp. 199–209. IEEE Computer Society Press, 1995.

    Google Scholar 

  19. U. Goltz and W. Reisig. The non-sequential behaviour of Petri nets. Inform. and Comput., 57:125–147, 1983.

    MATH  MathSciNet  Google Scholar 

  20. R. Janicki and M. Koutny. Semantics of inhibitor nets. Inform. and Comput., 123:1–16, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. Meseguer, Conditional rewriting logic as a unified model of concurrency, Theoretical Computer Science, 96:73–155, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  22. J. Meseguer. Rewriting logic as a semantic framework for concurrency: A progress report. In Proc. CONCUR’96, 7th International Conference on Concurrency Theory, (U. Montanari, V. Sassone, Eds.), vol. 1119 of Lect. Notes in Comput. Sci., pp. 331–372. Springer, 1996.

    Google Scholar 

  23. J. Meseguer and U. Montanari. Petri nets are monoids: A new algebraic foundation for net theory. In Proc. LICS’89, 3rd Symposium on Logic in Computer Science, pp. 155–164. IEEE Computer Society Press, 1988.

    Google Scholar 

  24. J. Meseguer and U. Montanari. Petri nets are monoids. Inform. and Comput., 88(2):105–155, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  25. J. Meseguer, U. Montanari, and V. Sassone. On the semantics of place/transition Petri nets. Math. Struct. in Computer Science, 7:359–397, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  26. U. Montanari and F. Rossi. Contextual occurrence nets and concurrent constraint programming. In Graph Transformations in Computer Science, vol. 776 of Lect. Notes in Comput. Sci., pp. 280–285. Springer, 1994.

    Google Scholar 

  27. U. Montanari and F. Rossi. Contextual nets. Acta Inform., 32:545–596, 1995.

    MATH  MathSciNet  Google Scholar 

  28. C.A. Petri. Kommunikation mit Automaten. Ph.D. thesis, Institut für Instrumentelle Mathematik, Bonn, 1962.

    Google Scholar 

  29. W. Reisig. Petri Nets: An Introduction. EACTS Monographs on Theoretical Computer Science. Springer, 1985.

    Google Scholar 

  30. G. Ristori. Modelling Systems with Shared Resources via Petri Nets. Ph.D. thesis, TD-5/94, Dipartimento di Informatica, Universitá di Pisa, 1994.

    Google Scholar 

  31. V. Sassone. An axiomatization of the algebra of Petri net concatenable processes. Theoretical Computer Science, 170:277–296, 1996.

    MATH  MathSciNet  Google Scholar 

  32. V. Sassone. An axiomatization of the category of Petri net computations. Math. Struct. in Computer Science, 8:117–151, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  33. M.-O. Stehr, J. Meseguer, and P.C. Olveczky. Rewriting logic as a unifying framework for Petri nets. This Volume.

    Google Scholar 

  34. W. Vogler. Efficiency of asynchronous systems and read arcs in Petri nets. In Proc. ICALP’97, 24th International Colloquium on Automata, Languages, and Programming, vol. 1256 of Lect. Notes in Comput. Sci., pp. 538–548. Springer, 1997.

    Google Scholar 

  35. W. Vogler. Partial order semantics and read arcs. In Proc. MFCS’97, 22nd Int. Symp. on Mathematical Foundations of Computer Science, (P. Degano, R. Gorrieri, A. Marchetti-Spaccamela, Eds.), vol. 1295 of Lect. Notes in Comput. Sci., pp. 508–517. Springer, 1997.

    Google Scholar 

  36. G. Winskel. Event structures. In Proc. of Advanced Course on Petri Nets, vol. 255 of Lect. Notes in Comput. Sci., pp. 325–392. Springer, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bruni, R., Sassone, V. (2001). Two Algebraic Process Semantics for Contextual Nets. In: Ehrig, H., Padberg, J., Juhás, G., Rozenberg, G. (eds) Unifying Petri Nets. Lecture Notes in Computer Science, vol 2128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45541-8_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-45541-8_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43067-4

  • Online ISBN: 978-3-540-45541-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics