Skip to main content
SpringerLink
Log in

LTL-Specification of Counter Machines

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

This article is written in support of the academic discipline “Nonclassical logics”. The objects of study within this discipline are the basic principles and constructive elements used in formal construction of various nonclassical propositional logics. Despite the abstract nature of the theory of nonclassical logics, which is mainly focused on strict mathematical formalization of logical reasoning, there are real practical applications for its theoretical results. In particular, languages of temporal modal logics are widely used for modeling, specification, and verification (correctness analysis) of logic control program systems. This article demonstrates, based on the example of linear temporal logic (LTL), how abstract concepts of nonclassical logics can be applied in practice in the area of information technology and programming. It is shown that the behavior of a software system can be represented as a set of LTL formulas, which can then be used to check the satisfiability of the properties of that software system via the procedure for proving the validity of logical inferences expressed in terms of linear temporal logic (LTL). The approach to using LTL to specify the behavior of software systems is demonstrated based on Minsky counter machines. Minsky machines are one of the ways of formalizing the intuitive concept of an algorithm. Their computational power is equivalent to that of Turing machines. A counter machine is a computer program written in a high-level language, since it contains variables called counters and conditional and unconditional jump operators used for loop construction. It is known that any algorithm can (hypothetically) be implemented as a three-counter Minsky machine.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

REFERENCES

  1. Kuzmin, E.V., Neklassicheskie logiki vyskazyvanii (Nonclassical Propositional Logics), Yaroslavl: Yaroslav. Gos. Univ. im. P.G. Demidova, 2016.

  2. Priest, G., An Introduction to Non-Classical Logic. From If to Is, Cambridge Introduction to Philosophy, Cambridge University Press, 2008, 2nd ed.

  3. Minsky, M., Computation: Finite and Infinite Machines, Englewood Cliffs, N.J.: Prentice-Hall, 1967.

    MATH  Google Scholar 

  4. Schroeppel, R., A two counter machine cannot calculate 2N, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 1972.

    Google Scholar 

  5. Kuzmin, E.V., Schetchikovye mashiny (Counter Machines), Yaroslavl: Yaroslav. Gos. Univ., 2010.

  6. Pnueli, A., The temporal logic of programs, 18th Ann. Symp. on Foundations of Computer Science (SFCS 1977), Providence, R.I., 1977, IEEE, 1977, pp. 46–57.  https://doi.org/10.1109/SFCS.1977.32

  7. Clarke, E.M., Grumberg, O., and Peled, D.A., Model Checking, Cambridge: The MIT Press, 2001.

    Book  MATH  Google Scholar 

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

    MATH  Google Scholar 

  9. Cadence SMV. http://www.kenmcmil.com/smv.html.

  10. Clarke, E., Grumberg, O., and Hamaguchi, K., Another look at LTL model checking, Tech. Rep. CMU-CS-94-114, Carnegie Mellon Univ., 1994.

  11. Kuzmin, E.V. and Sokolov, V.A., On construction and verification of PLC programs, Autom. Control Comput. Sci., 2013, vol. 47, no. 7, pp. 443–451.  https://doi.org/10.3103/S0146411613070110

    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.  https://doi.org/10.3103/S0146411614070244

    Article  Google Scholar 

  13. Kuzmin, E.V., Sokolov, V.A., and Ryabukhin, D.A., Construction and verification of PLC-programs by LTL-specification, Autom. Control Comput. Sci., 2015, vol. 49, no. 7, pp. 453–465.  https://doi.org/10.3103/S0146411615070159

    Article  Google Scholar 

  14. Kuzmin, E.V., Sokolov, V.A., and Ryabukhin, D.A., Construction and verification of PLC LD programs by the LTL specification, Autom. Control Comput. Sci., 2014, vol. 48, no. 7, pp. 424–436.  https://doi.org/10.3103/S014641161407013X

    Article  Google Scholar 

  15. 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.  https://doi.org/10.3103/S0146411614070256

    Article  Google Scholar 

  16. Kuzmin, E.V., Ryabukhin, D.A., and Sokolov, V.A., On the expressiveness of the approach to constructing PLC-programs by LTL-specification, Autom. Control Comput. Sci., 2016, vol. 50, no. 7, pp. 510–519.  https://doi.org/10.3103/S0146411616070130

    Article  Google Scholar 

Download references

Funding

This work was supported by Demidov Yaroslavl State University, project No. VIP-016.

Author information

Authors and Affiliations

  1. Demidov Yaroslavl State University, 150003, Yaroslavl, Russia

    E. V. Kuzmin

Authors
  1. E. V. Kuzmin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. V. Kuzmin.

Ethics declarations

The author declares that he has no conflicts of interest.

Additional information

Translated by A. Ovchinnikova

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuzmin, E.V. LTL-Specification of Counter Machines. Aut. Control Comp. Sci. 56, 711–722 (2022). https://doi.org/10.3103/S0146411622070112

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411622070112

Search

Navigation