Algebraic Theories for Contextual Pre-nets

  • Roberto Bruni
  • José Meseguer
  • Ugo Montanari
  • Vladimiro Sassone
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)


The algebraic models of computation for contextual nets that have been proposed in the literature either rely on a non-free monoid of objects, or introduce too many fictitious behaviors that must be somewhat filtered out. In this paper, we exploit partial membership equational logic to define a suitable theory of models, where the meaningful concurrent computations can be selected by means of membership predicates.


Algebraic Theory Monoidal Category Forgetful Functor Monoidal Functor Symmetric Monoidal Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baldan, P., Bruni, R., Montanari, U.: Pre-nets, read arcs and unfolding: a functorial presentation. In: Proc. WADT 2002. LNCS, Springer, Heidelberg (2003) (to appear)Google Scholar
  2. 2.
    Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures, and processes. Inform. and Comput. 171(1), 1–49 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bouhoula, A., Jouannaud, J.-P., Meseguer, J.: Specification and proof in membership equational logic. Theoret. Comput. Sci. 236, 35–132 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bruni, R., Gadducci, F.: Some algebraic laws for spans (and their connections with multirelations). In: Proc. RelMiS 2001. ENTCS, vol. 44.3, Elsevier, Amsterdam (2001)Google Scholar
  5. 5.
    Bruni, R., Meseguer, J., Montanari, U., Sassone, V.: Functorial models for petri nets. Inform. and Comput. 170(2), 207–236 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bruni, R., Meseguer, J., Montanari, U., Sassone, V.: Functorial models for contextual prenets. Technical Report TR-02-09, Computer Science Department, University of Pisa (2002)Google Scholar
  7. 7.
    Bruni, R., Sassone, V.: Two algebraic process semantics for contextual nets. In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) APN 2001. LNCS, vol. 2128, pp. 427–456. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Christensen, S., Hansen, N.D.: Coloured petri nets extended with place capacities, test arcs and inhibitor arcs. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 186–205. Springer, Heidelberg (1993)Google Scholar
  9. 9.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Quesada, J.: Maude: Specification and programming in rewriting logic. Th. Comput. Sci. 285, 187–243 (2002)zbMATHCrossRefGoogle Scholar
  10. 10.
    Crazzolara, F., Winskel, G.: Events in security protocols. In: Proc. CCS 2001, pp. 96–105. ACM Press, New York (2001)CrossRefGoogle Scholar
  11. 11.
    De Francesco, N., Montanari, U., Ristori, G.: Modeling concurrent accesses to shared datavia Petri nets. In: Programming Concepts, Methods and Calculi, IFIP Transactions A-56, pp. 403–422. North-Holland, Amsterdam (1994)Google Scholar
  12. 12.
    Degano, P., Meseguer, J., Montanari, U.: Axiomatizing the algebra of net computationsand processes. Acta Inform. 33(7), 641–667 (1996)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Gadducci, F., Montanari, U.: Axioms for contextual net processes. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 296–308. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  14. 14.
    van Glabbeek, R.J., Plotkin, G.D.: Configuration structures. In: Proc. LICS 1995, pp. 199–209. IEEE Computer Society Press, Los Alamitos (1995)Google Scholar
  15. 15.
    Goltz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Inform. and Comput. 57, 125–147 (1983)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Janicki, R., Koutny, M.: Semantics of inhibitor nets. Inf. and Comput. 123(1), 1–16 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Meseguer, J.: Rewriting logic as a semantic framework for concurrency: A progress report. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 331–372. Springer, Heidelberg (1996)Google Scholar
  18. 18.
    Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Google Scholar
  19. 19.
    Meseguer, J., Montanari, U.: Petri nets are monoids. Inf. and Comp. 88(2), 105–155 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Meseguer, J., Montanari, U.: Mapping tile logic into rewriting logic. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 62–91. Springer, Heidelberg (1998)Google Scholar
  21. 21.
    Meseguer, J., Montanari, U., Sassone, V.: Representation theorems for Petri nets. In: Freksa, C., Jantzen, M., Valk, R. (eds.) Foundations of Computer Science. LNCS, vol. 1337, pp. 239–249. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  22. 22.
    Meseguer, J., Ölveczky, P.C., Stehr, M.-O.: Rewriting logic as a unifying framework for Petri nets. In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) APN 2001. LNCS, vol. 2128, pp. 250–303. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  23. 23.
    Montanari, U., Rossi, F.: Contextual occurrence nets and concurrent constraint programming. In: Ehrig, H., Schneider, H.-J. (eds.) Dagstuhl Seminar 1993. LNCS, vol. 776, pp. 280–295. Springer, Heidelberg (1994)Google Scholar
  24. 24.
    Montanari, U., Rossi, F.: Contextual nets. Acta Inform. 32, 545–596 (1995)zbMATHMathSciNetGoogle Scholar
  25. 25.
    Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Institut für Instrumentelle Mathematik, Bonn (1962)Google Scholar
  26. 26.
    Reisig, W.: Petri Nets: An Introduction. EATCS Monographs. Springer, Heidelberg (1985)zbMATHGoogle Scholar
  27. 27.
    Sassone, V.: An axiomatization of the algebra of Petri net concatenable processes. Theoret. Comput. Sci. 170(1-2), 277–296 (1996)zbMATHMathSciNetGoogle Scholar
  28. 28.
    Sassone, V.: An axiomatization of the category of Petri net computations. Math. Struct. in Comput. Sci. 8(2), 117–151 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Vogler, W.: Efficiency of asynchronous systems and read arcs in Petri nets. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 538–548. Springer, Heidelberg (1997)Google Scholar
  30. 30.
    Vogler, W.: Partial order semantics and read arcs. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 508–517. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  31. 31.
    Winskel, G., Nielsen, M.: Models for concurrency. In: Handbook of Logic in Computer Science, Oxford University Press, Oxford (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Roberto Bruni
    • 1
  • José Meseguer
    • 2
  • Ugo Montanari
    • 1
  • Vladimiro Sassone
    • 3
  1. 1.Dipartimento di InformaticaUniversità di PisaItalia
  2. 2.University of Illinois at Urbana-ChampaignUSA
  3. 3.COGSUniversity of SussexBrightonUK

Personalised recommendations