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

  • Ievgen IvanovEmail author
  • Mykola Nikitchenko
  • Uri Abraham
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 469)


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.


Real-time system Cyber-physical system Dynamical system Continuous-time system Formal theory Decidability Verification 

Key Terms

Mathematical Model Specification Process Verification Process 



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


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ievgen Ivanov
    • 1
    • 2
    Email author
  • Mykola Nikitchenko
    • 1
  • Uri Abraham
    • 3
  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.Paul Sabatier UniversityToulouseFrance
  3. 3.Ben-Gurion UniversityBeer-ShevaIsrael

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