# Kleene Algebras and Semimodules for Energy Problems

@inproceedings{sik2013KleeneAA, title={Kleene Algebras and Semimodules for Energy Problems}, author={Zolt{\'a}n {\'E}sik and Ulrich Fahrenberg and Axel Legay and Karin Quaas}, booktitle={ATVA}, year={2013} }

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 Buchi acceptance for semiring-weighted automata, we show that these generalized energy problems are decidable. We also provide complexity results for…

## 13 Citations

### An ω-Algebra for Real-Time Energy Problems

- MathematicsArXiv
- 2017

A *-continuous Kleene ω-algebra of real-time energy functions which can be used to model systems which can consume and regain energy depending on available time.

### *-Continuous Kleene ω-Algebras for Energy Problems

- Mathematics, Computer ScienceFICS
- 2015

It is shown here that energy problems can be solved by algebraic manipulations on the transition matrix of energy automata, and general results about certain classes of finitely additive functions on complete lattices are proved.

### An omega-Algebra for Real-Time Energy Problems

- MathematicsFSTTCS
- 2015

A *-continuous Kleene omega-algebra of real-time energy functions which can be used to model systems which can consume and regain energy depending on available time.

### Verification for Timed Automata Extended with Unbounded Discrete Data Structures

- Computer ScienceCONCUR
- 2014

The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable and obtain a strong model that may be used to model real-time programs with procedure calls.

### *-Continuous Kleene $\omega$-Algebras

- Mathematics
- 2015

It is shown that *-continuous Kleene $\omega$-algebras give rise to iteration semiring-semimodule pairs and how this work can be applied to solve certain energy problems for hybrid systems.

### Well Behaved Transition Systems

- Computer ScienceLog. Methods Comput. Sci.
- 2017

The well-quasi-ordering that defines well-structured transition systems (WSTS) is shown not to be the weakest hypothesis that implies decidability of the coverability problem, and coverability decidable for monotone transition systems that only require the absence of infinite antichains.

### An Algebraic Approach to Energy Problems II - The Algebra of Energy Functions

- Computer Science, MathematicsActa Cybern.
- 2017

It is shown that energy functions form a *-continuous Kleene ω-algebra, as an application of a general result that finitely additive, locally *-closed and T-continuously functions on complete lattices form *- continuous Kleeneπ-algebras.

### Quantitative properties of featured automata

- Computer ScienceInternational Journal on Software Tools for Technology Transfer
- 2019

A model of featured weighted automata is introduced which combines featured transition systems and (semiring-) weighted automation and applications to minimum reachability and to energy properties are shown.

### *-Continuous Kleene ω-Algebras

- MathematicsDLT
- 2015

It is shown that \(^*\)-continuous Kleene \(\omega \)-algebras give rise to iteration semiring-semimodule pairs, and that for Buchi automata over \(*\)-continuous Kleinene algebra, one can compute the associated infinitary power series.

### Algebraic Derivation of Until Rules and Application to Timer Verification

- Computer ScienceRAMiCS
- 2018

Using correspondences betweenlinear temporal logic and modal Kleene Algebra, rules of linear temporal logic involving the until operator are proved in an algebraic manner in order to verify programmable logic controllers.

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