An algebraic approach to Energy Problems II the algebra of energy functions

Z. Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 cer tain tasks can be repeatedly accomplished and the system never runs out of energy (or other resources). In order to develop a general theory of energy problems, we introduce energy automata: Finite automata whose transitions are labeled with energy functions which specify how energy values change from one system state to another. We show that energy functions form a ∗-continuous Kleene ω-algebra, as an application of a general result that finitely additive, locally ∗-closed and T-continuous functions on complete lattices form ∗-continuous Kleene ω-algebras. This permits to solve energy problems in energy automata in a generic, algebraic way. In order to put our work in context, we also review extensions of energy problems to higher dimensions and to games.

Original languageEnglish
Pages (from-to)229-268
Number of pages40
JournalActa Cybernetica
Volume23
Issue number1
DOIs
Publication statusPublished - Jan 1 2017

Fingerprint

Algebraic Approach
Energy Function
Algebra
Energy
Kleene Algebra
Finite automata
Embedded systems
Automata
Energy Management
Complete Lattice
Infinite Systems
Finite Automata
Resource Management
Autonomous Systems
Embedded Systems
Higher Dimensions
Continuous Function
Schedule
Game
Closed

Keywords

  • Energy problem
  • Kleene algebra
  • ∗-continuity
  • ∗-continuous Kleene ω-algebra

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

An algebraic approach to Energy Problems II the algebra of energy functions. / Ésik, Z.; Fahrenberg, Uli; Legay, Axel; Quaas, Karin.

In: Acta Cybernetica, Vol. 23, No. 1, 01.01.2017, p. 229-268.

Research output: Contribution to journalArticle

Ésik, Z. ; Fahrenberg, Uli ; Legay, Axel ; Quaas, Karin. / An algebraic approach to Energy Problems II the algebra of energy functions. In: Acta Cybernetica. 2017 ; Vol. 23, No. 1. pp. 229-268.
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