An Algebraic Approach to Energy Problems I — *-Continuous Kleene ω-Algebras
| Autor: | Axel Legay, Zoltán Ésik, Karin Quaas, Uli Fahrenberg |
|---|---|
| Přispěvatelé: | UCL - SST/ICTM/INGI - Pôle en ingénierie informatique |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Information Systems and Management Kleene's recursion theorem 020207 software engineering 02 engineering and technology Management Science and Operations Research Theoretical Computer Science Kleene algebra Mathematics::Logic Computer Science::Logic in Computer Science Kleene star 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) 020201 artificial intelligence & image processing Computer Vision and Pattern Recognition Electrical and Electronic Engineering Algebraic number Computer Science::Formal Languages and Automata Theory Software Energy (signal processing) Mathematics |
| Zdroj: | Acta Cybernetica, Vol. 23, no.1, p. 203-228 (2017) |
| ISSN: | 0324-721X |
| DOI: | 10.14232/actacyb.23.1.2017.13 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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