Fixing Zeno Gaps

  • In computer science fixpoints play a crucial role. Most often least and greatest fixpoints are sufficient. However there are situations where other ones are needed. In this paper we study, on an algebraic base, a special fixpoint of the function f(x) = a · x that describes infinite iteration of an element a. We show that the greatest fixpoint is too imprecise. Special problems arise if the iterated element contains the possibility of stepping on the spot (e.g. skip in a programming language) or if it allows Zeno behaviour. We present a construction for a fixpoint that captures these phenomena in a precise way. The theory is presented and motivated using an example from hybrid system analysis.

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Metadaten
Author:Peter HöfnerGND, Bernhard MöllerGND
URN:urn:nbn:de:bvb:384-opus4-11809
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1449
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2010-11)
Type:Report
Language:English
Publishing Institution:Universität Augsburg
Release Date:2010/10/08
Tag:fixpoints; iteration; semiring; Kleene algebra; omega algebra; hybrid systems
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Fakultät für Angewandte Informatik / Institut für Informatik / Lehrstuhl für Datenbanken und Informationssysteme
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):Deutsches Urheberrecht