Advertisement

Concatenable graph processes: Relating processes and derivation traces

  • Paolo Baldan
  • Andrea Corradini
  • Ugo Montanari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1443)

Abstract

Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic double-pushout approach to graph rewriting, namely the derivation trace and the graph process semantics. The notion of concatenable graph process is introduced and then the category of concatenable derivation traces is shown to be isomorphic to the category of concatenable graph processes. As an outcome we obtain a quite intuitive characterization of events and configurations of the event structure associated to a graph grammar.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Baldan, A. Corradini, and U. Montanari. An event structure semantics for P/T contextual nets: Asymmetric event structures. FoSSaCS '98, LNCS 1378, pp. 63–80. Springer, 1998.Google Scholar
  2. 2.
    A. Corradini. Concurrent Graph and Term Graph Rewriting. CONCUR'96, LNCS 1119, pp. 438–464. Springer, 1996.Google Scholar
  3. 3.
    A. Corradini, H. Ehrig, M. Löwe, U. Montanari, and F. Rossi. Abstract Graph Derivations in the Double-Pushout Approach. Dagstuhl Seminar 9301 on Graph Transformations in Computer Science, LNCS 776, pp. 86–103. Springer, 1994.Google Scholar
  4. 4.
    A. Corradini, H. Ehrig, M. Löwe, U. Montanari, and F. Rossi. Note on standard representation of graphs and graph derivations. Dagstuhl Seminar 9301 on Graph Transformations in Computer Science, LNCS 776, pp. 104–118. Springer, 1994.Google Scholar
  5. 5.
    A. Corradini, H. Ehrig, M. Löwe, U. Montanari, and F. Rossi. An Event Structure Semantics for Graph Grammars with Parallel Productions. 5th International Workshop on Graph Grammars and their Application to Computer Science, LNCS 1073. Springer, 1996.Google Scholar
  6. 6.
    A. Corradini, U. Montanari, and F. Rossi. Graph processes. Fundamenta Informaticae, 26:241–265, 1996.MATHMathSciNetGoogle Scholar
  7. 7.
    A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Löwe. Algebraic Approaches to Graph Transformation I: Basic Concepts and Double Pushout Approach. In [15].Google Scholar
  8. 8.
    P. Degano, J. Meseguer, and U. Montanari. Axiomatizing the algebra of net computations and processes. Acta Informatica, 33:641–647, 1996.MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    H. Ehrig. Tutorial introduction to the algebraic approach of graph-grammars. 3rd International Workshop on Graph-Grammars and Their Application to Computer Science, LNCS 291, pp. 3–14. Springer, 1987.Google Scholar
  10. 10.
    U. Golz and W. Reisig. The non-sequential behaviour of Petri nets. Information and Control, 57:125–147, 1983.MathSciNetCrossRefGoogle Scholar
  11. 11.
    H.-J. Kreowski. Manipulation von Graphmanipulationen. PhD thesis, Technische Universität Berlin, 1977.Google Scholar
  12. 12.
    A. Maggiolo-Schettini and J. Winkowski. Dynamic Graphs. In MFCS'96, LNCS 1113, pp. 431–442, 1996.MathSciNetGoogle Scholar
  13. 13.
    J. Meseguer, U. Montanari, and V. Sassone. On the semantics of Petri nets. In CONCUR '92, LNCS 630, pp. 286–301. Springer, 1992.Google Scholar
  14. 14.
    J. Meseguer, U. Montanari, and V. Sassone. Process versus unfolding semantics for Place/Transition Petri nets. Theoret. Comput. Sci., 153(1–2):171–210, 1996.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    G. Rozenberg, editor. Handbook of Graph Grammars and Computing by Graph Transformation. Volume 1: Foundations. World Scientific, 1997.Google Scholar
  16. 16.
    G. Schied. On relating Rewriting Systems and Graph Grammars to Event Structures. Dagstuhl Seminar 9301 on Graph Transformations in Computer Science, LNCS 776, pp. 326–340. Springer, 1994.Google Scholar
  17. 17.
    G. Winskel. Event Structures. In Petri Nets: Applications and Relationships to Other Models of Concurrency, LNCS 255, pp. 325–392. Springer, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Paolo Baldan
    • 1
  • Andrea Corradini
    • 1
  • Ugo Montanari
    • 1
  1. 1.Dipartimento di InformationUniversity of PisaPisaItaly

Personalised recommendations