Automation and Remote Control

, Volume 75, Issue 8, pp 1369–1383 | Cite as

Paradigm of computations on the Petri nets

Models and Solution Methods for Problems in Theory of Scheduling

Abstract

The paradigm of computations on the Petri nets was shown to appreciably speed up the computations and reduce laboriousness of software development owing to the mass parallelism and asynchronous information processing. A language of the programmed Petri nets was developed, alternative approaches to realizing the paradigm at the micro and macro levels were proposed, and the estimates of complexity of the earlier universal Petri net that are prototypes of the corresponding processor were specified. Indicated were the lines of practical realization of the paradigm such as the development of the technology of programming on the loaded Petri net, technology of translation of the loaded Petri nets to the inhibitory Petri nets, and the efficient hardware processors executing programs in the language of the inhibitory Petri nets. Fast computations are supported by the nets of the Sleptsov class with multiple start of transition at a step.

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References

  1. 1.
    Peterson, J.L., Petri Net Theory and Modeling of Systems, Englewood Cliffs: Prentice-Hall, 1981. Translated under the title Teoriya setei Petri i modelirovanie sistem, Moscow: Mir, 1984.Google Scholar
  2. 2.
    Kotov, V.E., Seti Petri (Petri Nets), Moscow: Nauka, 1984.MATHGoogle Scholar
  3. 3.
    Sleptsov, A.I. and Yurasov, A.A., Avtomatizatsiya proektirovaniya upravlyayushchikh sistem gibkikh avtomatizirovannykh proizvodstv (Automated Design of the Control Systems for Flexible Computer-aided Manufacturing), Malinovskii, B.N., Ed., Kiev: Tekhnika, 1986.Google Scholar
  4. 4.
    Achasova, S.M. and Bandman, O.L., Korrektnost’ parallel’nykh vychislitel’nykh protsessov (Correctness of Parallel Computations), Novosibirsk: Nauka, 1990.MATHGoogle Scholar
  5. 5.
    Jensen, K., Colored Petri Nets. Basic Concepts, Analysis Methods and Practical Use, 3 vols., New York: Springer, 1997.Google Scholar
  6. 6.
    Lomazova, I.A., Vlozhennye seti Petri: modelirovanie i analiz raspredelennykh sistem s ob”ektnoi strukturoi (Emberdded Petri Nets: Modeling and Analysis of Distributed Systems with Object Sturucture), Moscow: Nauchnyi Mir, 2004.Google Scholar
  7. 7.
    Zaitsev, D.A., Clans of Petri Nets: Verification of Protocols and Performance Evaluation of Networks, Saarbrücken: LAP LAMBERT Acad. Publishing, 2013.Google Scholar
  8. 8.
    Peng, S.S. and Zhou, M.Ch., Petri Net Based PLC Stage Programming for Discrete-event Control Design, in Systems, Man, and Cybernetics, 2001 IEEE Int. Conf., 2001, vol. 4, pp. 2706–2710.CrossRefGoogle Scholar
  9. 9.
    Rossmann, J. and Eilers, K., Translating Robot Programming Language Flow Control into Petri Nets, in Emerging Technologies and Factory Automation (ETFA), 2011 IEEE 16th Conf. Digital Object Identifier, 2011, pp. 1–7.Google Scholar
  10. 10.
    Palomeras, N., Ridao, P., Carreras, M., et al., Using Petri Nets to Specify and Execute Missions for Autonomous Underwater Vehicles, in Intelligent Robots and Systems, IROS 2009, IEEE/RSJ Int. Conf., Oct. 10–15, 2009, pp. 4439–4444.CrossRefGoogle Scholar
  11. 11.
    Dodd, R.B., Coloured Petri Net Modelling of a Generic Avionics Mission Computer, Air Operations Division: Defence Science and Technology Organisation, Australia, DSTO-TN-0692, 2006.Google Scholar
  12. 12.
    Usher, M. and Jackson, D., A Petri Net Based Visual Programming Language, in Systems, Man, and Cybernetics, 1998. IEEE Int. Conf., 1998, vol. 1, pp. 107–112.CrossRefGoogle Scholar
  13. 13.
    Iordache, M.V. and Antsaklis, P.J., Petri Nets and Programming: A Survey, in Am. Control Conf. 2009, ACC’09, 2009, pp. 4994–4999.CrossRefGoogle Scholar
  14. 14.
    Voevodin, V.V. and Voevodin, Vl.V., Parallel’nye vychisleniya (Parallel Computations) St. Petersburg: BKnV-Peterburg, 2002.Google Scholar
  15. 15.
    Zaitsev, D.A., Universal Petri Net, Kibern. Sist. Anal., 2012, no. 4, pp. 24–39.Google Scholar
  16. 16.
    Zaitsev, D.A., Toward the Minimal Universal Petri Net, IEEE Trans. Syst., Man, Cybernet., 2014, vol. 44, no. 1, pp. 47–58.CrossRefGoogle Scholar
  17. 17.
    Zaitsev, D.A., Inhibitory Petri Net Executing an Arbitrary Defined Turing Machine, Sist. Doslidzh. Inform. Tekhnol., 2012, no. 2, pp. 26–41.Google Scholar
  18. 18.
    Zaitsev, D.A., Inhibitory Petri Net Executing an Arbitrary Defined Normal Markov Algorithm, Modelir. Anal. Inform. Sist., 2011, vol. 18, no. 4, pp. 80–93.Google Scholar
  19. 19.
    Sleptsov, A.I., State Equations and Equivalent Transformations of Loaded Petri Nets (Algebraic Approach), in Formal Models of Parallel Computation, Proc. All-Union Conf., Novosibirsk, 1988, pp. 151–158.Google Scholar
  20. 20.
    Zaitsev, D.A. and Sleptsov, A.I., State Equation and Equivalent Transformations of the Time Petri Nets, Kibern. Sist. Anal., 1997, no. 5, pp. 59–76.Google Scholar
  21. 21.
    Zaitsev, D.A., Small Polynomial Time Universal Petri Nets, arXiv:1309.7288.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.International Humanitarian UniversityOdessaUkraine

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