Section: New Results

Energy-Centric Systems

Participants : Axel Legay, Uli Fahrenberg.

This part is concerned with Tasks 1 and 2. Mostly, we focus on quantifying properties of interconnected objects such as Cyber Physical Systems (CPS) (SoS and CPS share a lot of commonalities).

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 (1) certain tasks can be repeatedly accomplished and (2) the system never runs out of energy (or other specified resources). Formal modeling and analysis of such problems has attracted some attention in recent years.

[18] (C; accepted)

We define and study basic properties of ${}^{*}$-continuous Kleene $\omega$-algebras that involve a ${}^{*}$-continuous Kleene algebra with a ${}^{*}$-continuous action on a semimodule and an infinite product operation that is also ${}^{*}$-continuous. We show that ${}^{*}$-continuous Kleene $\omega$-algebras give rise to iteration semiring-semimodule pairs, and that for Büchi automata over ${}^{*}$-continuous Kleene $\omega$-algebras, one can compute the associated infinitary power series.

[17] (C; accepted)

Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on ${}^{*}$-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.

[15] (C; accepted)

We develop a ${}^{*}$-continuous Kleene $\omega$-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 $\omega$-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.