 
Summary: Carrying Probabilities to the Infinite World
Parosh Aziz Abdulla
Uppsala University, Sweden
Abstract. We give en exampleguided introduction to a framework that
we have developed in recent years in order to extend the applicability of
program verification to the context of systems modeled as infinitestate
Markov chains. In particular, we describe the class of decisive Markov
chains, and show how to perform qualitative and quantitative analysis of
Markov chains that arise from probabilistic extensions of classical models
such as Petri nets and communicating finitestate processes.
1 Introduction
In recent years, several approaches have been proposed for automatic verification
of infinitestate systems (see e.g., [2, 1]). In a parallel development, there has been
an extensive research effort for the design and analysis of models with stochastic
behaviors (e.g., [12, 7, 6, 11]). Recently, several works have considered verification
of infinitestate Markov chains that are generated by pushdown systems (e.g.,
[9, 10]). We consider verification of Markov chains with infinite state spaces. We
describe a general framework that can handle probabilistic versions of several
classical models such as Petri nets and communicating finitestate processes. We
do that by defining abstract conditions on infinite Markov chains that give rise
