Graph grammars for distributed systems

  • Ilaria Castellani
  • Ugo Montanari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 153)


In the paper we define grammars on a class of labeled, partially ordered hypergraphs, called distributed systems. A distributed system models both the spatial and the temporal aspects of a real system through the relations of adjacency and causality. Terminal symbols represent the (deterministic, certain) past history of the system while nonterminal symbols model the (possibly nondeterministic, potential) future history of the system. The (context free) productions of a grammar represent the possible stand-alone evolutions of system components. From the productions, we obtain a (possibly infinite) number of rewriting rules, which model the synchronized evolution of adjacent system components. The (terminal) distributed systems derived within a given grammar represent the alternative deterministic, concurrent computations of a single nondeterministic system which is thus completely modeled by the grammar.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /1/.
    E.Astesiano, G.Reggio, E.Zucca. Operational Frameworks for Semantic Description of Concurrent Languages, with an application to ADA-like languages, Internal Report CNET-61, Dept. of Mathematics, Univ. of Genova.Google Scholar
  2. /2/.
    R.Milner. A Calculus of Communicating Systems, Springer LNCS n∘ 92, 1980.Google Scholar
  3. /3/.
    R.Milner. Calculi for Synchrony and Asynchrony, Internal Report CSR-104-82, Edinburgh University, February 1982Google Scholar
  4. /4/.
    C.A.R.Hoare, S.D.Brookes, A.W.Roscoe. A Theory of Communicating Sequential Processes, Technical Monograph PRG-16, Programming Research Group, Oxford University, 1981.Google Scholar
  5. /5/.
    C.A.Petri. Concurrency, Proc. Net Theory and Applications, Springer LNCS n∘ 84, 1980, pp. 251–260.Google Scholar
  6. /6/.
    C.A.R. Hoare. Communicating Sequential Processes, Comm. ACM 21, August 1978, pp. 666–677.Google Scholar
  7. /7/.
    M.Nielsen, G.Plotkin, G.Winskel. Petri nets, event structures and domains, part 1, TCS 13, 1981.Google Scholar
  8. /8/.
    G.Winskel. Event structure semantics for CCS and related languages, ICALP '82, Springer LNCS n∘ 140, July 1982.Google Scholar
  9. /9/.
    J.Winkowski. Behaviours of Concurrent Systems, TCS 11, 1980, pp. 39–60.Google Scholar
  10. /10/.
    U.Montanari, C.Simonelli. On Distinguishing Concurrency from Nondeterminism, Proc. Réseaux de Petri et Parallélisme, Colleville sur mer, May 1980.Google Scholar
  11. /11/.
    I.Castellani, P.Franceschi, U.Montanari. Labeled Event Structures: A Model for Observable Concurrency, IFIP TC 2 — Working Conference: Formal Description of Programming Concepts II, Garmisch — Partenkirchen, June 1982, NorthHolland, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Ilaria Castellani
    • 1
  • Ugo Montanari
    • 1
  1. 1.Istituto di Scienze dell'InformazioneUniversity of PisaItaly

Personalised recommendations