Coreflective Concurrent Semantics for Single-Pushout Graph Grammars

  • Paolo Baldan
  • Andrea Corradini
  • Ugo Montanari
  • Leila Ribeiro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2755)


The problem of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets has been faced several times along the years, both for the single-pushout and double-pushout approaches, but only partial results were obtained. In this paper we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of graph grammars and the category of prime algebraic domains.


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  1. 1.
    Baldan, P.: Modelling concurrent computations: from contextual Petri nets to graph grammars. PhD thesis, Department of Computer Science, University of Pisa, Available as technical report n. TD-1/00 (2000)Google Scholar
  2. 2.
    Baldan, P., Corradini, A., Montanari, U.: An event structure semantics for P/T contextual nets: Asymmetric event structures. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 63–80. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Baldan, P., Corradini, A., Montanari, U.: Unfolding of double-pushout graph grammars is a coreflection. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) TAGT 1998. LNCS, vol. 1764, pp. 145–163. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Baldan, P., Corradini, A., Montanari, U.: Contextual Petri nets, asymmetric event structures and processes. Information and Computation 171(1), 1–49 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Corradini, A.: Concurrent graph and term graph rewriting. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 438–464. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  7. 7.
    Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Padberg, J.: The category of typed graph grammars and its adjunctions with categories of derivations. In: Cuny, J., Engels, G., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1994. LNCS, vol. 1073. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundamenta Informaticae 26, 241–265 (1996)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic Approaches to Graph Transformation I: Basic Concepts and Double Pushout Approach. In: Rozenberg [25], ch. 3Google Scholar
  10. 10.
    Ehrig, H., Habel, A., Kreowski, H.-J., Parisi-Presicce, F.: Parallelism and concurrency in High-Level Replacement Systems. Mathematical Structures in Computer Science 1, 361–404 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic Approaches to Graph Transformation II: Single Pushout Approach and Comparison with Double Pushout Approach. In: Rozenberg [25], ch. 4Google Scholar
  12. 12.
    Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: an algebraic approach. In: Proc. of IEEE Conf. on Automata and Switching Theory, pp. 167–180 (1973)Google Scholar
  13. 13.
    Golz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Information and Control 57, 125–147 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Heckel, R., Corradini, A., Ehrig, H., Löwe, M.: Horizontal and vertical structuring of graph transformation systems. Mathematical Structures in Computer Science 6(6), 613–648 (1996)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Janicki, R., Koutny, M.: Semantics of inhibitor nets. Information and Computation 123, 1–16 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Korff, M.: Generalized graph structure grammars with applications to concurrent object-oriented systems. PhD thesis, Technische Universität Berlin (1996)Google Scholar
  17. 17.
    Langerak, R.: Transformation and Semantics for LOTOS. PhD thesis, Department of Computer Science, University of Twente (1992)Google Scholar
  18. 18.
    Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoretical Computer Science 109, 181–224 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Löwe, M., Korff, M., Wagner, A.: An Algebraic Framework for the Transformation of Attributed Graphs. In: Term Graph Rewriting: Theory and Practice, pp. 185–199. Wiley, London (1993)Google Scholar
  20. 20.
    Meseguer, J., Montanari, U., Sassone, V.: On the semantics of Place/Transition Petri nets. Mathematical Structures in Computer Science 7, 359–397 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Montanari, U., Rossi, F.: Contextual nets. Acta Informatica 32(6) (1995)Google Scholar
  22. 22.
    Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85–108 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Pinna, G.M., Poigné, A.: On the nature of events: another perspective in concurrency. Theoretical Computer Science 138(2), 425–454 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Ribeiro, L.: Parallel Composition and Unfolding Semantics of Graph Grammars. PhD thesis, Technische Universität Berlin (1996)Google Scholar
  25. 25.
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1. World Scientific, Singapore (1997)zbMATHGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Paolo Baldan
    • 1
  • Andrea Corradini
    • 2
  • Ugo Montanari
    • 2
  • Leila Ribeiro
    • 3
  1. 1.Dipartimento di InformaticaUniversità Ca’ Foscari di VeneziaItalia
  2. 2.Dipartimento di InformaticaUniversità di PisaItalia
  3. 3.Instituto de InformáticaUniversidade Federal do Rio Grande do SulBrazil

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