Cybernetics and Systems Analysis

, Volume 48, Issue 4, pp 498–511 | Cite as

Universal petri net

  • D. A. Zaitsev


A universal inhibitor Petri net executing an arbitrary given inhibitor Petri net is constructed. An inhibitor Petri net graph, its marking, and transition firing sequence are encoded as 10 scalar nonnegative integer variables and are represented by the corresponding places of the universal net. An algorithm using only these scalar variables and executing an arbitrary inhibitor net is developed based on the state equation and is encoded by the universal inhibitor Petri net. Subnets that implement arithmetic, comparison, and copy operations are employed.


universal inhibitor Petri net universal Turing machine algorithm encoding control flow 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Agerwala, “A complete model for representing the coordination of asynchronous processes,” Hopkins Computer Science Program, Res. Rep., No. 32, John Hopkins University, Baltimore (1974).Google Scholar
  2. 2.
    V. E. Kotov, Petri Nets [in Russian], Nauka, Moscow (1984).Google Scholar
  3. 3.
    Rolf Herken (ed.), The Universal Turing machine: A half-century survey, Springer, Wien–New York (1994).Google Scholar
  4. 4.
    D. A. Zaitsev “Universal inhibitor Petri net,” in: Proc. 17th German Workshop on Algorithms and Tools for Petri Nets, Cottbus, Germany (2010), pp. 1–15.Google Scholar
  5. 5.
    A. I. Sleptsov and A. A. Yurasov, Automation of Designing Control Systems of Flexible Computer-Aided Productions [in Russian], Tekhnika, Kiev (1986).Google Scholar
  6. 6.
    A. I. Sleptsov, “State equations and equivalent transformations of loaded Petri nets (algebraic approach),” in: Proc. and Comm. of All-Union Conf. “Formal Models of Parallel Computations,” Novosibirsk (1988), pp. 151–158.Google Scholar
  7. 7.
    D. A. Zaizev, “Compositional analysis of Petri nets,” Cybernetics and Systems Analysis, Vol. 42, No. 1, 126–136 (2006).Google Scholar
  8. 8.
    D. A. Zaitsev, “Complexity of a universal inhibitor Petri net,” in: Proc. 18th German Workshop on Algorithms and Tools for Petri Nets, Hagen, Germany (2011), pp. 62–71.Google Scholar
  9. 9.
    M. Minsky, “Size and structure of universal Turing machines using tag systems,” in: Recursive Function Theory, Symposium in Pure Mathematics, Vol. 5, AMS, Provelence (1962), pp. 229–238.Google Scholar
  10. 10.
    Y. Rogozhin, “Small universal Turing machines,” TCS, Vol. 168, No. 2, 215–240 (1996).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.International Humanitarian UniversityOdessaUkraine

Personalised recommendations