Skip to main content
Log in

Automating the Conversion of Colored Petri Nets with Qualitative Tokens Into Colored Petri Nets with Quantitative Tokens

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The authors describe an algorithm for conversion of colored Petri nets with qualitative tokens into a colored Petri net with quantitative tokens preserving boundedness, mutual exclusion, and liveness properties. This conversion allows the invariance method to be applied to colored Petri nets, which uses the Truncated Set of Solutions finding algorithm for Petri net state equations expressed through systems of linear homogenous Diophantine equations. To show the algorithm’s efficiency, it is applied to the colored Petri net that models the operation of a grid system. Equivalence of net models is tested by constructing and analyzing equal finite-state machine.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Jensen and L. M. Kristensen, Coloured Petri Nets, Modelling and Validation of Concurrent Systems, Springer, Berlin (2009).

  2. W. M. P. Van der Aalst and C. Stahl, Modeling Business Processes — A Petri Net-Oriented Approach, The MIT Press, Cambridge (2011).

    MATH  Google Scholar 

  3. S. A. Chernenok and V. A. Nepomniaschy, “The application of coloured Petri nets to verification of distributed systems specified by message sequence charts,” in: Proc. ISP RAS, Vol. 27, No. 3 (2015), pp. 197–218.

  4. “Examples of industrial use of CP-nets,” URL: http://www.daimi.au.dk/CPnets/intro/example_indu.html.

  5. K. Jensen, L. M. Kristensen, and L. Wells, “Coloured Petri nets and CPN Tools for modelling and validation of concurrent systems,” Intern. J. on Software Tools for Technology Transfer, Vol. 9, No. 3–4, 213–254 (2007).

    Article  Google Scholar 

  6. D. O. Romannikov and A. V. Markov, “Using the CPN Tools software package for the analysis of Petri nets,” A Collection of Sci. Works of NSTU, No. 2, 105–116 (2012).

  7. ProM 6.6, URL: http://www.promtools.org/doku.php?id=prom66.

  8. K. Schmidt, “LoLA: A low level analyzer,” in: Proc. 21th Intern. Conf. on Application and Theory of Petri Nets (June 26–30, 2000, Aarhus, Denmark), Springer-Verlag, Heidelberg (2000), pp. 465–474.

  9. S. L. Kryvyi, “Calculating the minimum set of invariants of a Petri net,” Iskusstv. Intellekt, No. 3, 199–206 (2001).

  10. S. L. Kryvyi, Linear Diophantine Constraints and their Application [in Ukrainian], Bukrek, Chernivtsi–Kyiv (2015).

    Google Scholar 

  11. S. L. Kryvyi and L. E. Matveeva, “Applying Petri nets to solve some telecommunication problems,” Iskusstv. Intellekt, No. 3, 590–598 (2002).

  12. L. E. Matveeva, “An automatic system of the analysis and verification of the telecommunication system described in MSC language, by means of the formalism of Petri nets,” Problemy Program., No. 2–3, 108–117 (2004).

  13. E. A. Lukyanova and A. V. Dereza, “Investigating single-type structural elements of a component Petri net during component modeling and analysis of a complex system with parallelism,” Cybern. Syst. Analysis, Vol. 48, No. 6, 823–831 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Yu. Shelestov, “Modeling a grid node based on Petri nets,” Systemni Doslidzh. ta Inform. Tekhnologii, No. 3, 52–65 (2009).

    Google Scholar 

  15. K. Jensen, “Coloured Petri nets and the invariant method,” Theoretical Computer Science, Vol. 14, 317–336 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  16. D. K. Hlomozda, “Applying the method of invariants to the analysis of colored Petri nets,” Naukovi Zapysky NAUKMA, Komp. Nauky, Vol. 177, 44–52 (2015).

  17. D. K. Hlomozda, “Applying the method of invariants to the analysis of colored Petri nets with deadlocks,” Visnyk NTUU “KPI.” Informatyka, Upravlinnya ta Obchysl. Tekhnika, No. 64, 38–46 (2016).

  18. S. L. Kryvyi, Y. V. Boiko, S. D. Pogorilyy, O. F. Boretskyi, and M. M. Glybovets, “Design of grid structures on the basis of transition systems with the substantiation of the correctness of their operation,” Cybern. Syst. Analysis, Vol. 53, No. 1, 105–114 (2017).

    Article  MATH  Google Scholar 

  19. K. Jensen, CPN Tools State Space Manual, Univ. of Aarhus, Aarhus (2002).

  20. AT&T FSM Library 4.0, URL: https://www3.cs.stonybrook.edu/~algorith/implement/fsm/implement.shtml.

  21. S. Gordon, “Converting coloured Petri net state space to finite state automata,” CPNTools, FSM and Lextools (2013). URL: https://sandilands.info/sgordon/cpntools-fsm-lextools.

  22. D. K. Hlomozda, “CpnToUnit utility,” URL: https://github.com/Gyrotank/CpnUnitTransformer.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. K. Hlomozda.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2018, pp. 151–163.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hlomozda, D.K., Glybovets, M.M. & Maksymets, O.M. Automating the Conversion of Colored Petri Nets with Qualitative Tokens Into Colored Petri Nets with Quantitative Tokens. Cybern Syst Anal 54, 650–661 (2018). https://doi.org/10.1007/s10559-018-0066-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-018-0066-4

Keywords

Navigation