Kleene Algebras and Semimodules for Energy Problems

With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce generalized energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Uncovering a close connection between energy problems and reachability and B\"uchi acceptance for semiring-weighted automata, we show that these generalized energy problems are decidable. We also provide complexity results for important special cases

*-Continuous Kleene ω\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.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Verification for Timed Automata extended with Unbounded Discrete Data Structures

We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance be used to model real-time programs with procedure calls. It is long known that the reachability problem for this model is decidable. The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable

Energiautomater, energifunktioner og Kleene-algebra

Forfatterne til denne artikel har, sammen med mange gode kolleger, i en del år arbejdet med såkaldte energiproblemer. Disse handler om, at man i en formel model ønsker at bestemme, om der findes en endelig eller uendelig eksekvering under hvilken en given energivariabel aldrig bliver negativ. Den formelle model kan være en vægtet tidsautomat, en endelig automat som er annoteret med energifunktioner eller lignende. Fælles for alle disse modeller er, at det har vist sig ualmindeligt svært at løse sådanne energiproblemer og at teknikker fra Kleene-algebra har været en stor hjælp.  Formålet med denne artikel er at give et overblik over nylig forskning i energiproblemer (for første gang på dansk) samt at udvide anvendelsen af Kleene-algebra i et forsøg på at lukke et åbent problem fra artiklen som startede hele dette område.&nbsp