An $\omega$-Algebra for Real-Time Energy Problems

Abstract

We develop a * -continuous Kleene ω-algebra of real-time energy functions. Together with corresponding automata, these can be used to model systems which can consume and regain energy (or other types of resources) depending on available time. Using recent results on * -continuous Kleene ω-algebras and computability of certain manipulations on real-time energy functions, it follows that reachability and Büchi acceptance in real-time energy automata can be decided in a static way which only involves manipulations of real-time energy functions. This is a revised and extended version of the paper [CFL15] which has been presented at the 35th IARCS Annual Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2015) in Bangalore, India. Compared to [CFL15], and in addition to numerous small changes and improvements, motivation and examples as well as proofs of all results have been added to the paper.Most of this work was completed while the second author was still employed at Irisa / Inria Rennes. LOGICAL METHODS lI N COMPUTER SCIENCE