An algebraic approach to energy problems II - the algebra of energy functions

  • Zoltán Ésik
  • Uli Fahrenberg
  • Axel Legay
  • Karin Quaas


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.


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How to Cite
Ésik, Z., Fahrenberg, U., Legay, A., & Quaas, K. (2017). An algebraic approach to energy problems II - the algebra of energy functions. Acta Cybernetica, 23(1), 229-268.
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