*-Continuous Kleene $omega$-Algebras for Energy Problems

Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the transition matrix of energy automata. To this end, we prove general results about certain classes of finitely additive functions on complete lattices which should be of a more general interest.

💡 Research Summary

The paper addresses the verification of energy‑related properties in embedded and autonomous systems by introducing a robust algebraic framework based on *‑continuous Kleene ω‑algebras. An “energy automaton” is defined as a finite‑state machine whose transitions are labeled with partial functions that model how the system’s energy level changes when moving between states. These energy functions are defined on intervals (