Advertisement

Automatic Control and Computer Sciences

, Volume 51, Issue 7, pp 507–515 | Cite as

Derivation of the Cascade Parallel Composition of Timed Finite State Machines Using BALM-II

  • M. L. Gromov
  • N. V. Shabaldina
Article

Abstract

The paper considers the problem of deriving a cascade parallel composition of timed finite state machines (TFSMs). It can be reduced to a step-by-step derivation of a binary parallel composition. It is known that if each component of the binary parallel composition is a TFSM with constant output delays, then the composition can result in a TFSM with an infinite set of output delays given by a finite set of linear functions. Therefore, the problem of deriving a cascade composition of TFSMs with constant output delays is reduced to deriving a series of binary parallel compositions of TFSMs with output delays given either as constants or as a set of linear functions. In this paper, we refine the definition of the TFSM with particular attention to the description of the output delay. BALM-II is used as an instrument for deriving the composition. Therefore, we consider the transition from a TFSM with output delays given as a set of linear functions to the corresponding automaton. We propose a new procedure for deriving an automaton. Unlike the known procedure, it does not require subsequent determinization of the derived automaton. In addition, we provide a step-by-step description of how to derive the composition of the corresponding automata using BALM-II, discuss the procedure of reverse transformation from the automaton of the composition to the TFSM, and note some aspects associated with the composition of TFSMs with output delays as a set of linear functions. An example that illustrates the derivation of the cascade parallel composition of TFSMs is given.

Keywords

timed finite state machines cascade parallel composition BALM-II 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Moore, E.F., Gedanken-experiments on Sequential Machines, Autom. Stud., Ann. Math. Stud., 1956, vol. 34, pp. 129–153.MathSciNetGoogle Scholar
  2. 2.
    Gill, A., Introduction to the Theory of Finite-State Machines, New York: McGraw-Hill, 1962.MATHGoogle Scholar
  3. 3.
    Yevtushenko, N., Villa, T., Brayton, R., Petrenko, A., and Sangiovanni-Vincentelli, A., Solution of parallel language equations for logic synthesis, The Proceedings of the International Conference on Computer-Aided Design, 2001, pp. 103–110.Google Scholar
  4. 4.
    Castagnetti, G., Piccolo, M., Villa, T., Yevtushenko, N., Mishchenko, A., and Brayton, R.K., Solving Parallel Equations with BALM-II, Technical Report No UCB/EECS-2012-181, Electrical Engineering and Computer Sciences University of California at Berkeley, 2012. http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-181.pdf.Google Scholar
  5. 5.
    Alur, R. and Dill, D.L., A theory of timed automata, Theor. Comput. Sci., 1994, vol. 126, no. 2, pp. 183–235.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    El-Fakih, K., Gromov, M., Shabaldina, N., and Yevtushenko, N., Distinguishing experiments for timed nondeterministic finite state machines, Acta Cybern., 2013, vol. 21, no. 2, pp. 205–222.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Kondratyeva, O., Yevtushenko, N., and Cavalli, A., Parallel composition of nondeterministic finite state machines with timeouts, J. Control Comput. Sci. Tomsk State Univ., 2014, vol. 2, no. 27, pp. 73–81.Google Scholar
  8. 8.
    Kondratyeva, O., Yevtushenko, N., and Cavalli, A., Solving parallel equations for Finite State Machines with Timeouts, Proc. ISP RAS, 2014, vol. 26, no. 6, pp. 85–98.CrossRefGoogle Scholar
  9. 9.
    http://www.uppaal.com/.Google Scholar
  10. 10.
    Zhigulin, M., Yevtushenko, N., Maag, S., and Cavalli, A.R., FSM-based test derivation strategies for systems with timeouts, Proceedings of the International Conference QSIC, 2011, pp. 141–149.Google Scholar
  11. 11.
    Gromov, M. and Shabaldina, N., Using BALM-II for deriving parallel composition of timed finite state machines with outputs delays and timeouts: work-in-progress, Syst. Inf., 2016, vol. 8, pp. 33–42.Google Scholar
  12. 12.
    Springintveld, J., Vaandrager, F., and D’Argenio, P.R., Testing timed automata, Theor. Comput. Sci., 2001, vol. 254, nos. 1–2, pp. 225–257.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia

Personalised recommendations