TY  - RPRT
A1  - Höfner, Peter
A1  - Möller, Bernhard
T1  - Fixing zeno gaps
N2  - 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.
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2010-11 
KW  - fixpoints
KW  - iteration
KW  - semiring
KW  - Kleene algebra
KW  - omega algebra
KW  - hybrid systems
Y1  - 2010
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/1449
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-11809
PB  - Institut für Informatik, Universität Augsburg
CY  - Augsburg
ER  -