A note on the attractor-property of infinite-state Markov chains
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 - Delta for some positive Delta, 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. (c) 2005 Elsevier B.V. All rights reserved.
theory of computation attractors in markov chains verification of probabilistic systems lossy channel systems