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C. Baier, N. Bertrand, Ph. Schnoebelen. A note on the attractor-property of infinite-state Markov chains. Information Processing Letters, 97(2):58-63, January 2006.

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In the past 5 years, a series of verification algorithms has been proposed for infinite Markov chains that have a finite attractor, i.e., a set that will be visited infinitely often almost surely starting from any state. In this paper, we establish a sufficient criterion for the existence of an attractor. We show that if the states of a Markov chain can be given levels (positive integers) such that the expected next level for states at some level n>0 is less than n-Δ for some positive Δ, then the states at level 0 constitute an attractor for the chain. As an application, we obtain a direct proof that some probabilistic channel systems combining message losses with duplication and insertion errors have a finite attractor


Nathalie Bertrand http://www.irisa.fr/prive/nbertran/

BibTex Reference

   Author = {Baier, C. and Bertrand, N. and Schnoebelen, Ph.},
   Title = {A note on the attractor-property of infinite-state {M}arkov chains},
   Journal = {Information Processing Letters},
   Volume = {97},
   Number = {2},
   Pages = {58--63},
   Publisher = {Elsevier Science Publishers},
   Month = {January},
   Year = {2006}

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