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Brief Announcement: Computing Automatically the Stabilization Time Against the Worst and the Best Schedules

  • Joffroy Beauquier
  • Colette Johnen
  • Stéphane Messika
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4167)

Abstract

In this paper, we reduce the problem of computing the convergence time for a randomized self-stabilizing algorithm to an instance of the stochastic shortest path problem (SSP). The solution gives us a way to compute automatically the stabilization time against the worst and the best policy. Moreover, a corollary of this reduction ensures that the best and the worst policy for this kind of algorithms are memoryless and deterministic. We apply these results here in a toy example. We just present here the main results, to more details, see [1].

Keywords

Markov Chain Markov Decision Process Stabilization Time Convergence Time Computation Step 
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.

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References

  1. 1.
    Beauquier, J., Johnen, C., Messika, S.: Computing automatically the stabilization time against the worst and the best schedulers. Technical Report 1448, L.R.I (2006)Google Scholar
  2. 2.
    Bertsekas, D.P., Tsitsiklis, J.N.: An analysis of stochastic shortest path problems. Math. of Op. Res. 16(2), 580–595 (1991)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    de Alfaro, L.: Formal Verification of Probabilistic systems. Ph.D Thesis, Stanford University (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joffroy Beauquier
    • 1
  • Colette Johnen
    • 1
  • Stéphane Messika
    • 1
  1. 1.L.R.I./C.N.R.S.Université Paris-Sud 11 

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