An algebraic approach to energy problems I - continuous Kleene ω-algebras ‡

Energy problems are important in the formal analysis of embedded or autonomous systems. With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce energy automata. These are finite automata whose edges are labeled with energy functions that define ho...

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Bibliographic Details
Main Authors: Ésik Zoltán
Fahrenberg Uli
Legay Axel
Quaas Karin
Format: Article
Published: 2017
Series:Acta cybernetica 23 No. 1
Kulcsszavak:Kleene - algebra, Matematika, Stephen Cole Kleene
Subjects:
doi:10.14232/actacyb.23.1.2017.14

Online Access:http://acta.bibl.u-szeged.hu/50071
Description
Summary:Energy problems are important in the formal analysis of embedded or autonomous systems. With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Motivated by this application and in order to compute with energy functions, we introduce a new algebraic structure of *-continuous Kleene ω-algebras. These involve a *-continuous Kleene algebra with a *-continuous action on a semimodule and an infinite product operation that is also *-continuous. We define both a finitary and a non-finitary version of *-continuous Kleene ω-algebras. We then establish some of their properties, including a characterization of the free finitary *-continuous Kleene ω-algebras. We also show that every *-continuous Kleene ω-algebra gives rise to an iteration semiring-semimodule pair.
Physical Description:203-228
ISSN:0324-721X