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].
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References
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)
Bertsekas, D.P., Tsitsiklis, J.N.: An analysis of stochastic shortest path problems. Math. of Op. Res. 16(2), 580–595 (1991)
de Alfaro, L.: Formal Verification of Probabilistic systems. Ph.D Thesis, Stanford University (1997)
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© 2006 Springer-Verlag Berlin Heidelberg
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Beauquier, J., Johnen, C., Messika, S. (2006). Brief Announcement: Computing Automatically the Stabilization Time Against the Worst and the Best Schedules. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_40
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DOI: https://doi.org/10.1007/11864219_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44624-8
Online ISBN: 978-3-540-44627-9
eBook Packages: Computer ScienceComputer Science (R0)