Concurrent probabilistic program, or: How to schedule if you must

  • Sergiu Hart
  • Micha Sharir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)


Given a finite set of concurrent processes executing asynchronously, such that each process may use randomization in its course of execution, we consider the problem of computing the worst-case probability for the program which consists of these processes to terminate (i.e, to converge to a specified set of common goal states), under a fair interleaving scheduling of the processes. Several methods for computing this probability are presented, and characterizations of the special case in which this probability is 1 are derived. Specializations of these characterizations to the case of deterministic and nondeterministic programs are also discussed.


Subharmonic Function Concurrent Process Converse Inequality Fair Schedule Synchronization Protocol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [DS]
    L.E. Dubins and L.J. Savage, “Inequalities fox Stochastic Processes; How to Gamble if You Must”, Dover, N.Y. 1976.Google Scholar
  2. [HSP]
    S. Hart, M.Sharir and A. Pnueli, “Termination of Concurrent Probabilistic Programs”, Proc. 9th POPL Conference, 1982, pp. 1–7. (also to appear in TOPLAS 1983).Google Scholar
  3. [LPS]
    D. Lehmann, A. Pnueli and J. Stavi, “Impartiality, Justice, Fairness: The Ethics of Concurrent Termination”, Proc. 8th ICALP Conference, 1981, pp. 264–277.Google Scholar
  4. [LR]
    D. Lehmann and M.O. Rabin, “On the Advantages of Free Choice: A Symmetric and Fully Distributed Solution to the Dining Philosophers' Problem”, Proc. 8th POPL Conference, 1981, pp. 133–138.Google Scholar
  5. [Ra1]
    M.O. Rabin, “N Process Synchronization by a 4 log2N — valued Shared Variable”, JCSS 25 (1982) pp. 66–75.Google Scholar
  6. [Ra2]
    M.O. Rabin, “The Choice Coordination Problem” Acta Informatica 17 (1982) pp.121–134.Google Scholar
  7. [RS1]
    J.Reif and P. Spirakis, “Distributed Algorithms for Synchronizing Interprocess Communication Within Real Time”, Proc. 13th STOC Conference, 1981, pp. 133–145.Google Scholar
  8. [RS2]
    J.Reif and P. Spirakis, “Unbounded Speed Variability in Distributed Communication Systems”, Proc. 9th POPL Conference, 1982, pp. 46–56.Google Scholar
  9. [SPH]
    M.Sharir, A. Pnueli and S. Hart, “The verification of Probabilistic Programs”, to appear in SIAM J. Computing.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Sergiu Hart
    • 1
  • Micha Sharir
    • 1
  1. 1.School of Mathematical SciencesTel-Aviv UniversityIsrael

Personalised recommendations