Infinite-State Verification: From Transition Systems to Markov Chains

We present a general framework which can handle probabilistic versions of several classical models such as Petri nets, lossy channel systems, push-down automata, and noisy Turing machines.First, we describe algorithms for verification of \emph{well quasi-orderedtransition systems}. These are transition systems which are monotonic w.r.t. a well quasi-ordering on the state space. Then, we extend the framework by introducing decisive Markov chains, a class of Markov chains which cover all the above mentioned models. We consider both safety and liveness problems for decisive Markov chains. Safety: What is the probability that a given set of states is eventually reached. Liveness: What is the probability that a given set of states is reached infinitely often}. We will also consider limiting behaviors for infinite-state Markov chains.

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