On priorities of parallelism: Petri nets under the maximum firing strategy

  • Hans-Dieter Burhard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 148)


The computational power of Petri nets is extended up to the power of counter machines by realizing certain priorities of parallelism. Hence certain concurrent computations can not exactly be reflected by the sets of all sequentialized computations in related systems. Moreover, the reachability, boundedness and liveness problems are undecidable under the modified firing rule.


Turing Machine Reachability Graph Firing Sequence Firable Transition Fair Schedule 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /B1/.
    Burkhard, H.D., Ordered Firing in Petri Nets, Elektron.Informationsverarb.Kybernetik 17(1981)2/3, 71–86.Google Scholar
  2. /B2/.
    Burkhard, H.D., Two Pumping Lemmata for Petri Nets. To appear in Elektron.Informationsverarb.Kybernetik.Google Scholar
  3. /H1/.
    Hack, M., Decision Problems for Petri Nets and Vector Addition Systems, MAC-TM 59, Proj.MAC, M.I.T. 1975.Google Scholar
  4. /H2/.
    Hack, M., Petri net languages, CSG Memo 124, Proj.MAC, M.I.T. 1975.Google Scholar
  5. /HP/.
    Hopcroft, J., Pansiot, J.J., On the reachability problem for 5-dimensional vector addition systems, Theor.Comp.Science 8(1979), 135–159.Google Scholar
  6. /JLL/.
    Jones, N., Landweber, L., Lien, E., Complexity of some problems in Petri nets, Theor.Comp.Science 4(1977), 277–299.Google Scholar
  7. /KM/.
    Karp, R.M., Miller, R.E., Parallel Program Schemata, Journ. Comp. and System Sciences 3(1969), 147–195.Google Scholar
  8. /K1/.
    Keller, R.M., Vector replacement systems: a formalism for modelling asynchronous systems, Tech.Rep.117, Comp.Science Lab., Princeton Univ., 1972/74.Google Scholar
  9. /K2/.
    Keller, R.M., Generalized Petri nets as models for system verification, Tech.Rep.202, Dept.Electrical Eng., Princeton Univ., 1975.Google Scholar
  10. /MATTK/.
    Mori, M., Araki, T., Taniguchi, K., Tokura, N., Kasami, T., Some decision problems for time Petri nets and applications to the verification of communication protocols, Trans.IECE'77/10 Vol.J60-D, No. 10, 822–829.Google Scholar
  11. /MPS/.
    Moalla, M., Pulou, J., Sifakis, J., Synchronized Petri nets: A model for the description of non-autonomous systems, Lecture Notes in Computer Science 64(1978), 374–384.Google Scholar
  12. /SM/.
    Salwicki, A., Müldner, T., On algorithmic properties of concurrent programs, Manuscript, Warsaw 1979.Google Scholar
  13. /V/.
    Valk, R., Self-modifying nets, a natural extension of Petri nets, Lecture Notes in Computer Science 62(1978), 464–476.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Hans-Dieter Burhard
    • 1
  1. 1.Sektion MathematikHumboldt-UniversitätBerlin

Personalised recommendations