Verifying continuous time Markov chains

  • Adnan Aziz
  • Kumud Sanwal
  • Vigyan Singhal
  • Robert Brayton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1102)


We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number theory.


Model Check Algebraic Number Continuous Time Markov Chain Discrete Time Markov Chain State Formula 
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  1. 1.
    R. Alur, C. Courcoubetis, and D. Dill. Model Checking for Real-Time Systems. In Proc. IEEE Symposium on Logic in Computer Science, pages 414–425, 1990.Google Scholar
  2. 2.
    R. Alur, C. Courcoubetis, and D. Dill. Model Checking for Probabilistic Real Time Systems. In Proc. of the Colloquium on Automata, Languages, and Programming, pages 115–126, 1991.Google Scholar
  3. 3.
    C. Courcoubetis and M. Yannakakis. Verifying Temporal Properties of Finite State Probabilistic Programs. In Proc. IEEE Symposium on the Foundations of Computer Science, pages 338–345, 1988.Google Scholar
  4. 4.
    E. A. Emerson. Temporal and Modal Logic. In J. van Leeuwen, editor, Formal Models and Semantics, volume B of Handbook of Theoretical Computer Science, pages 996–1072. Elsevier Science, 1990.Google Scholar
  5. 5.
    J. H. Ewing. Numbers. Springer-Verlag, 1991.Google Scholar
  6. 6.
    H. Hansson and B. Jonsson. A Logic for Reasoning about Time and Reliability. Formal Aspects of Computing, 6:512–535, 1994.CrossRefGoogle Scholar
  7. 7.
    T. Kaliath. Linear Systems. Prentice-Hall, 1980.Google Scholar
  8. 8.
    I. Niven. Irrational Numbers. John-Wiley, 1956.Google Scholar
  9. 9.
    S. Ross. Stochastic Processes. Wiley, 1983.Google Scholar
  10. 10.
    H. L. Royden. Real Analysis. Macmillan Publishing, 1989.Google Scholar
  11. 11.
    A. Tarski. A Decision Procedure for Elementary Algebra and Geometry. University of California Press, 1951.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Adnan Aziz
    • 1
  • Kumud Sanwal
    • 2
  • Vigyan Singhal
    • 3
  • Robert Brayton
    • 4
  1. 1.ECE UT AustinUSA
  2. 2.Bell Labs AT&TUSA
  3. 3.CBL CadenceUSA
  4. 4.EECS UC BerkeleyUSA

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