Carrying Probabilities to the Infinite World

We give en example-guided 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 infinite-state 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 finite-state processes.