Energy-parity objectives combine ω-regular with quantitative objectives of reward MDPs. The controller needs to avoid to run out of energy while satisfying a parity objective.
@inproceedings{MayrSTW17,
title = {MDPs with energy-parity objectives},
author = {Richard Mayr and Sven Schewe and Patrick Totzke and Dominik Wojtczak},
booktitle = {LICS},
year = {2017},
doi = {10.1109/lics.2017.8005131}
}