Advertisement

Structure Theory of Petri Nets: the Free Choice Hiatus

  • Eike Best
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 254)

Abstract

Structure theory asks whether a relationship can be found between the behaviour of a marked net and the structure of the underlying unmarked net. From the rich body of structure theoretical results that exists in Petri net theory, this paper selects a few examples which are deemed to be typical. The class of free choice nets, whose structure theory is particularly agreeable, is studied in some detail.

Keywords

Structure Theory Free Choice Transition Sequence Simple Cycle Strong Connectedness 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    G. Berthelot and R. Terrat: Petri Nets for the Correctness of Protocols. IEEE Trans. Comm. 30, 2497–2505 (1982).MathSciNetCrossRefGoogle Scholar
  2. [2]
    E. Best: Adequacy Properties of Path Programs. TCS Vol. 18, 149–171 (1982).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Best: COSY: its Relation to Nets and to CSP. These Notes.Google Scholar
  4. [4]
    E. Best: Fairness and Conspiracies. IPL Vol. 18, 215–220 (1984).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    E. Best and R. Devillers: Concurrent Behaviour: Sequences, Processes and Programming Languages. Studien der GMD No. 99 (1985). A revised version of this report is due to appear in TCS (1987).Google Scholar
  6. [6]
    E. Best and C. Fernández: Notations and Terminology on Petri Net Theory. Arbeitspapiere der GMD No. 195 (1986). Also: Petri Net Newsletters No. 23, 21-46 (April 1986).Google Scholar
  7. [7]
    E. Best and M. W. Shields: Some Equivalence Results on Free Choice Nets and Simple Nets, and on the Periodicity of Live Free Choice Nets. Springer Lecture Notes in Computer Science Vol. 159, 141–154 (1983).MathSciNetCrossRefGoogle Scholar
  8. [8]
    E. Best and P. S. Thiagarajan: (Forthcoming paper.)Google Scholar
  9. [9]
    E. Best and K. Voss: Free Choice Systems have Home States. Acta Informatica 21, 89–100 (1984).MathSciNetCrossRefGoogle Scholar
  10. [10]
    S. D. Brookes and W. C. Rounds: Behavioural Equivalence Notions Induced by Programming Logic. Springer Lecture Notes in Computer Science Vol. 154, 97–108 (1983).MathSciNetCrossRefGoogle Scholar
  11. [11]
    F. Commoner: Deadlocks in Petri Nets. Report, Applied Data Inc., CA-7206-2311 (1972).Google Scholar
  12. [12]
    F. Commoner, A. W. Holt, S. Even and A. Pnueli: Marked Directed Graphs. JCSS Vol. 5, 511–523 (1971).MathSciNetzbMATHGoogle Scholar
  13. [13]
    J. Desel: (Forthcoming paper in Petri Net Newsletters.)Google Scholar
  14. [14]
    K. Döpp: Zum Hack’schen Wohlformungssatz für Free-Choice-Petrinetze. EIK 19/1-2, 3–15 (1983).Google Scholar
  15. [15]
    K. Döpp: Ein Satz über Free-Choice-Petrinetze. EIK 19/3, 107–113 (1983).Google Scholar
  16. [16]
    A. Finkel: Boundedness and Liveness for Monogenous FIFO Nets and for Free Choice FIFO Nets — Applications to the Analysis of Protocols. Univ. Paris-Sud, L. R. I. Report No. 205 (1985).Google Scholar
  17. [17]
    H. J. Genrich and K. Lautenbach: Synchronisationsgraphen. Acta Informatica Vol. 2, 143–161 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    H. J. Genrich, K. Lautenbach and P. S. Thiagarajan: Elements of General Net Theory. Springer Lecture Notes in Computer Science Vol. 84, 21–163 (1981).MathSciNetCrossRefGoogle Scholar
  19. [19]
    H. J. Genrich and P. S. Thiagarajan: A Theory of Bipolar Synchronisation Schemes. TCS Vol. 30, 241–318 (1984).MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    W. Griese: Liveness in NSC Nets. In: Discrete Structures and Algorithms (ed. U. Pape), Carl Hanser Verlag, Munich, 256–264 (1980).Google Scholar
  21. [21]
    M. Hack: Analysis of Production Schemata by Petri Nets. TR-94, MIT-MAC (1972).Google Scholar
  22. [22]
    M. Hack: Corrections to MAC-TR-94. Computation Structure Notes 17, MIT-MAC (1974).Google Scholar
  23. [23]
    M. Hack: Extended State-Machine Allocatable Nets, an Extension of Free Choice Petri Net Results. Computation Structures Group Memo 78-1, MIT-MAC (1974).Google Scholar
  24. [24]
    D. Hillen: Relationship between Deadlock-freeness and Liveness in Free Choice Nets. Petri Net Newsletters No. 19, 28–32 (1985).Google Scholar
  25. [25]
    A. W. Holt: State Machines and Information. MIT-MAC Report (1970).Google Scholar
  26. [26]
    M. Jantzen and R. Valk: Formal Properties of Place/Transition-Nets. Springer Lecture Notes in Computer Science Vol. 84, 165–212 (1981).MathSciNetCrossRefGoogle Scholar
  27. [27]
    R. Johnsonbaugh and T. Murata: Additional Methods for Reduction and Expansion of Marked Graphs. IEEE Tr. on Circuits and Systems, Vol. 28/10, 1009–1014 (1981).MathSciNetCrossRefGoogle Scholar
  28. [28]
    K. Lautenbach: Linear Algebraic Techniques for Place/transition Nets. These Notes.Google Scholar
  29. [29]
    G. Memmi: Fuites et graphes à choix non imposé dans les réseaux de Petri. 3ème coll. int. sur la programmation, Dunod-Paris (1978).Google Scholar
  30. [30]
    G. Memmi: Leakage Notion. Springer Informatik-Fachberichte No. 52, 172–177 (1982).CrossRefGoogle Scholar
  31. [31]
    R. Milner: A Calculus of Communicating Systems. Springer Lecture Notes in Computer Science Vol. 92 (1980).Google Scholar
  32. [32]
    H. Müller: Prompt and hangup-free simulation of place/transition nets by pure nets without multiple arcs. Petri Net Newsletters No. 15, 16–21 (October 1983).Google Scholar
  33. [33]
    M. Nielsen and P. S. Thiagarajan: Degrees of Nondeterminism and Concurrency: A Petri Net View. DAIMI PB-180, University of Århus (1984). Also: 4th Conf. on Foundations of Software Technology and Theoretical Computer Science, Springer Lecture Notes in Computer Science, 89-117 (1984).Google Scholar
  34. [34]
    D. Park: Concurrency and Automata on Finite Sequences. Computer Science Department, University of Warwick (1981).Google Scholar
  35. [35]
    C. A. Petri: Nonsequential Processes. GMD-ISF Report 77. 05 (1977).Google Scholar
  36. [36]
    L. Pornello: Some Equivalence Notions for Concurrent Systems: An Overview. Arbeitspapiere der GMD No. 103 (1984). Also: Springer Lecture Notes in Computer Science Vol. 222, 381-400 (1985).Google Scholar
  37. [37]
    L. Priese: Automata and Concurrency. TCS Vol. 25(3), 221–265 (1982).MathSciNetCrossRefGoogle Scholar
  38. [38]
    W. Reisig: Petri Nets — An Introduction. Springer EATCS Monographs (1985).Google Scholar
  39. [39]
    W. Reisig: Place/transition Systems. These Notes.Google Scholar
  40. [40]
    M. W. Shields: On the Nonsequential Behaviour of Systems Possessing a Generalised Free Choice Property. Report CRS-92-81, Edinburgh University (1981).Google Scholar
  41. [41]
    P. S. Thiagarajan and K. Voss: A Fresh Look at Free Choice Nets. Information and Control, Vol. 61/2, 85–113 (1984).MathSciNetCrossRefGoogle Scholar
  42. [42]
    K. Voss: System Specification with Labelled Nets and the Notion of Interface Equivalence. Arbeitspapiere der GMD No. 211 (June 1986).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Eike Best
    • 1
  1. 1.Institut für methodische GrundlagenGesellschaft für Mathematik und DatenverarbeitungSt.AugustinGermany

Personalised recommendations