@article{Ésik_Fahrenberg_Legay_Quaas_2017, title={An algebraic approach to energy problems II - the algebra of energy functions}, volume={23}, url={https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3924}, DOI={10.14232/actacyb.23.1.2017.14}, abstractNote={Energy and resource management problems are important in areas such as embedded systems or autonomous systems. They are concerned with the question whether a given system admits infinite schedules during which certain tasks can be repeatedly accomplished and the system never runs out of energy (or other resources). In order to develop a general theory of energy problems, we introduce energy automata: finite automata whose transitions are labeled with energy functions which specify how energy values change from one system state to another. We show that energy functions form a *-continuous Kleene ω-algebra, as an application of a general result that finitely additive, locally *-closed and T-continuous functions on complete lattices form *-continuous Kleene ω-algebras. This permits to solve energy problems in energy automata in a generic, algebraic way. In order to put our work in context, we also review extensions of energy problems to higher dimensions and to games.}, number={1}, journal={Acta Cybernetica}, author={Ésik, Zoltán and Fahrenberg, Uli and Legay, Axel and Quaas, Karin}, year={2017}, month={Jan.}, pages={229-268} }