Aiming low is harder: induction for lower bounds in probabilistic program verification

@article{Hark2020AimingLI,
title={Aiming low is harder: induction for lower bounds in probabilistic program verification},
author={M. Hark and Benjamin Lucien Kaminski and Jurgen Giesl and J. Katoen},
journal={Proceedings of the ACM on Programming Languages},
year={2020},
volume={4},
pages={1 - 28}
}

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to be applied only finitely often in order to verify that the candidates are indeed lower bounds. In particular, it is not necessary to find the limit of a sequence as in many previous rules.