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On a Decidable Formal Theory for Abstract Continuous-Time Dynamical Systems

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Information and Communication Technologies in Education, Research, and Industrial Applications (ICTERI 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 469))

Abstract

We propose a decidable formal theory which describes high-level properties of abstract continuous-time dynamical systems called Nondeterministic Complete Markovian Systems (NCMS). NCMS is a rather general class of systems which can represent discrete and/or continuous evolutions in continuous time and which is sufficient for modeling a wide range of real-time information processing and cyber-physical systems (CPS). We illustrate the obtained results with a proof of the mutual exclusion property of a CPS which implements Peterson’s algorithm.

This work was supported in part by the research project No. 11BF015-02 “Formal specifications and methods of development of reliable software systems”, Taras Shevchenko National University of Kyiv, Ukraine.

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Acknowledgments

We would like to thank Dr. Martin Strecker and Prof. Louis FĂ©raud of Institut de Recherche en Informatique de Toulouse (IRIT), France for the ideas which inspired this work.

Author information

Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Ievgen Ivanov & Mykola Nikitchenko

  2. Paul Sabatier University, Toulouse, France

    Ievgen Ivanov

  3. Ben-Gurion University, Beer-Sheva, Israel

    Uri Abraham

Authors
  1. Ievgen Ivanov
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  2. Mykola Nikitchenko
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  3. Uri Abraham
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Corresponding author

Correspondence to Ievgen Ivanov .

Editor information

Editors and Affiliations

  1. Zaporizhzhya National University, Zaporizhzhya, Ukraine

    Vadim Ermolayev

  2. Institute of Applied Informatics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Heinrich C. Mayr

  3. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Mykola Nikitchenko

  4. Kherson State University, Kherson, Ukraine

    Aleksander Spivakovsky

  5. V.N. Karazin Kharkiv National University, Kharkov, Ukraine

    Grygoriy Zholtkevych

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Ivanov, I., Nikitchenko, M., Abraham, U. (2014). On a Decidable Formal Theory for Abstract Continuous-Time Dynamical Systems. In: Ermolayev, V., Mayr, H., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2014. Communications in Computer and Information Science, vol 469. Springer, Cham. https://doi.org/10.1007/978-3-319-13206-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-13206-8_4

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