# Abstract

We consider infinite-state discrete Markov chains which are *eager*: the probability of avoiding a defined set of final states for more than *n* steps is bounded by some exponentially decreasing function *f(n)*. We prove that eager Markov chains include those induced by Probabilistic Lossy Channel Systems, Probabilistic Vector Addition Systems with States, and Noisy Turing Machines, and that the bounding function *f(n)* can be effectively constructed for them. Furthermore, we study the problem of computing the expected reward (or cost) of runs until reaching the final states, where rewards are assigned to individual runs by computable reward functions. For eager Markov chains, an effective path exploration scheme, based on forward reachability analysis, can be used to approximate the expected reward up-to an arbitrarily small error.

This is an extended version of a conference presentation of the following paper:

*Parosh Aziz Abdulla, Noomene Ben Henda, Richard Mayr, Sven Sandberg. Eager Markov Chains. In proceeding of the 4th International Symposium on Automated Technology for Verification and Analysis (ATVA). Volume 4218 of LNCS. Pages 24-38. October 2006.*

A technical report version of the paper is available here.

The slides are here: ppt (2226 KB)