Advertisement

Constraints and extensions in a Calculus of EN systems

  • Giorgio De Michelis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 674)

Abstract

In this paper the domain of EN Systems is characterized as a Partial Order, by means of an injective morphism notion.

The partial order that is introduced has a behavioural interpretation in the sense that ‘larger’ Systems have ‘larger’ behavioural possibilities.

Then some unary operations are defined allowing to add Places and/or Transitions to an existing EN System. On the defined Partial Order the operation of adding a Transition is interpreted as enlarging the behaviour of the System (Extension), while the operation of adding a Place is interpreted as restricting it (Constraint).

Some properties of the two operation types are investigated.

The newly proposed order and operations are fully consistent with the semantics of EN Systems in terms of Elementary Transition Systems as defined in [NRT90].

Keywords

Elementary Net Systems Elementary Transition Systems Net Morphisms unary operations on nets Regions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References LNCS stands for Lecture Notes in Computer Sciences, Springer Verlag, Berlin.

  1. [BDDPRS91]
    L. Bernardinello, G. De Michelis, C. Diamantini, L. Pomello, A. Restelli, C. Simone, Relationships between Categories of “Elementary” Concurrent Systems. DSI Tech. Report, 1991Google Scholar
  2. [BDH90]
    E. Best, F. De Cindio, R. P. Hopkins, DEMON — Design Methods Based on Nets, An ESPRIT Basic Research Action (no. 3148). Bullettin of the EATCS, nr. 41, 1991Google Scholar
  3. [BRG87]
    W. Brauer, W. Reisig, G. Rozenberg (eds.), Petri Nets: Central Models and Their Properties. LNCS 254, 1987.Google Scholar
  4. [DDPS88]
    F. De Cindio, G. De Michelis, L. Pomello, C. Simone, A State Transformation Equivalence for Concurrent Systems: Exhibited Functionality Equivalence, in F. H. Vogt (ed.), CONCURRENCY 88, LNCS 335, 1988.Google Scholar
  5. [Dem92]
    G. De Michelis, Morphisms and Refinements for EN-Systems. DSI Tech. Report, 1992Google Scholar
  6. [ER90a]
    A. Ehrenfeucht, G. Rozenberg, Partial (Set) 2-Structures — Part 1: Basic Notion and the Representation Problem. Acta Informatica vol. 26, 1990.Google Scholar
  7. [ER90b]
    A. Ehrenfeucht, G. Rozenberg, Partial (Set) 2-Structures — Part 2: State Spaces of Concurrent Systems. Acta Informatica vol. 26, 1990.Google Scholar
  8. [MM88]
    S. J. Meseguer, U. Montanari, Petri Nets are Monoids. SRI-CSL-88-3, january 1988.Google Scholar
  9. [Mil80]
    R. Milner, A Calculus for Communicating Systems, LNCS 92, 1980Google Scholar
  10. [NRT90]
    M. Nielsen, G. Rozenberg, P. S. Thiagarajan, Elementary Transition Systems. Tech. Report, Dept. of Computer Science, University of Leiden, 1990.Google Scholar
  11. [PRS92]
    L. Pomello, C. Simone, A Survey of Equivalence Notions for Net based Systems. LNCS 609, 1992Google Scholar
  12. [PS91]
    L. Pomello, C. Simone, A State Transformation Preorder over a class of EN-Systems, in APN'90, LNCS 483, 1991.Google Scholar
  13. [PS92]
    L. Pomello, C. Simone, Concurrent Systems as Local State Transformation Algebras: the Case of Elementary Net Systems, Formal Aspects of Computing, 1992 (to appear).Google Scholar
  14. [Roz87]
    G. Rozenberg. Behaviour of Elementary Net Systems, in [BRG87].Google Scholar
  15. [RT86]
    G. Rozenberg, P.S. Thiagarajan, Petri Nets: basic notions, structure, behaviour, in J. W. de Bakker, W. P. de Roever, G. Rozenberg (eds.), Current Trends in Concurrency, LNCS 224, 1986.Google Scholar
  16. [Thi87]
    P.S. Thiagarajan, Elementary Net Systems, in [BRG87].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Giorgio De Michelis
    • 1
  1. 1.Dipartimento di Scienze dell'InformazioneUniversità degli Studi di MilanoMilanoItaly

Personalised recommendations