Skolem and positivity completeness of ergodic Markov chains

Mihir Vahanwala

Abstract: Highlights•We consider reachability problems that view Markov Chains as Linear Dynamical Systems (LDS).•We reduce number-theoretically hard problems for Linear Recurrence Sequences (LRS) to Markov Reachability Problems.•We map LRS of order k to ergodic Markov Chains with k+1 states.•This reduction is significant because restricting the order or spectrum often mitigates the hardness of verifying LDS.