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On the expressiveness of the approach to constructing PLC-programs by LTL-specification

Automatic Control and Computer Sciences volume 50, pages 510–519 (2016)Cite this article

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Abstract

The article is devoted to an approach to constructing and verification of discrete PLC-programs by LTL-specification. This approach provides a possibility of analysing the correctness of PLCprograms by using the model checking method. The linear temporal logic LTL is used as a language of specification of the program behavior. The correctness analysis of LTL-specification is automatically performed by the symbolic model checking tool Cadence SMV. The article demonstrates the consistency of the approach to constructing and verification of PLC programs by LTL-specification from the point of view of Turing power. It is proved that in accordance with this approach for any Minsky counter machine an LTL-specification can be built, which is used for machine implementation in any PLC programming language of standard IEC 61131-3. Minsky machines are equipollent to Turing machines, and the considered approach also has the Turing power. The proof focuses on representation of a counter machine behavior in the form of a set of LTL-formulas and matching these formulas to constructions of ST and SFC languages. SFC is interesting as a specific graphical language. ST is considered as a basic language because the implementation of a counter machine on IL, FBD/CFC and LD languages is reduced to rewriting blocks of an ST-program. The idea of the proof is demonstrated by an example of a Minsky 3-counter machine, which implements a function of squaring.

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References

  1. Kuzmin, E.V., Ryabukhin, D.A., and Sokolov, V.A., Modeling a consistent behavior of PLC-sensors, Model. Anal. Inf. Syst., 2014, vol. 21, no. 4, pp. 75–90.

    Google Scholar 

  2. Ryabukhin, D.A., Kuzmin, E.V., and Sokolov, V.A., Construction of PLC IL-programs by LTL-specification, Model. Anal. Inf. Syst., 2014, vol. 21, no. 2, pp. 26–38.

    Google Scholar 

  3. Kuzmin, E.V., Sokolov, V.A., and Ryabukhin, D.A., Construction and verification of PLC LD-programs by LTL-specification, Model. Anal. Inf. Syst., 2013, vol. 20, no. 6, pp. 78–94.

    Google Scholar 

  4. Kuzmin, E.V., Sokolov, V.A., and Ryabukhin, D.A., Construction and verification of PLC-programs by LTLspecification, Model. Anal. Inf. Syst., 2013, vol. 20, no. 4, pp. 5–22.

    Google Scholar 

  5. Kuzmin, E.V. and Sokolov, V.A., Modeling, specification and construction of PLC-programs, Model. Anal. Inf. Syst., 2013, vol. 20, no. 2, pp. 104–120.

    Google Scholar 

  6. Minsky, M., Computation: Finite and Infinite Machines, Prentice-Hall, Inc., 1967.

    MATH  Google Scholar 

  7. Petrov, I.V., Programmiruemye kontrollery. Standartnye yazyki i priemy prikladnogo proektirovaniya (Programmable Controllers. Standard Languages and Techniques of Applied Design), Moscow: SOLON-Press, 2004.

    Google Scholar 

  8. Baier, C. and Katoen, J.-P., Principles of Model Checking, The MIT Press, 2008.

    MATH  Google Scholar 

  9. Clark, E.M., Grumberg, O., and Peled, D.A., Model Checking, The MIT Press, 2001.

    Book  Google Scholar 

  10. CoDeSys, Controller Development System. http://www.3s-software.com/.

  11. Kuzmin, E.V., Sokolov, V.A., and Ryabukhin, D.A., Construction and verification of PLC LDprograms by the LTL Specification, Autom. Control Comput. Sci., 2014, vol. 48 no. 7, pp. 424–436.

    Article  Google Scholar 

  12. Kuzmin, E.V. and Sokolov, V.A., Modeling, specification and construction of PLC-programs, Autom. Control Comput. Sci., 2014, vol. 48, no. 7, pp. 554–563.

    Article  Google Scholar 

  13. Kuzmin, E.V., Ryabukhin, D.A., and Sokolov, V.A., Modeling a consistent behavior of PLC-sensors, Autom. Control Comput. Sci., 2014, vol. 48, no. 7, pp. 602–614.

    Article  Google Scholar 

  14. Parr, E.A., Programmable Controllers. An Engineer’s Guide, Newnes, 2003.

    Book  Google Scholar 

  15. Schroeppel, R., A Two Counter Machine Cannot Calculate 2N, Memo 257, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, 1972.

    Google Scholar 

  16. SMV, The Cadence SMV Model Checker. http://www.kenmcmil.com/smv.html.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia

    E. V. Kuzmin, D. A. Ryabukhin & V. A. Sokolov

Authors
  1. E. V. Kuzmin
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  2. D. A. Ryabukhin
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  3. V. A. Sokolov
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Corresponding author

Correspondence to E. V. Kuzmin.

Additional information

Original Russian Text © E.V. Kuzmin, D.A. Ryabukhin, V.A. Sokolov, 2015, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2015, Vol. 22, No. 4, pp. 507–520.

The article was translated by the authors.

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Kuzmin, E.V., Ryabukhin, D.A. & Sokolov, V.A. On the expressiveness of the approach to constructing PLC-programs by LTL-specification. Aut. Control Comp. Sci. 50, 510–519 (2016). https://doi.org/10.3103/S0146411616070130

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  • DOI: https://doi.org/10.3103/S0146411616070130

Keywords

  • programmable logic controllers (PLC)
  • construction and verification of PLC-programs
  • LTL-specification
  • Minsky counter machines