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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| Author: | Peter HöfnerGND, Bernhard MöllerGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-389096 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/38909 |
| Parent Title (English): | Theoretical Computer Science |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2011 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2018/07/23 |
| Volume: | 412 |
| Issue: | 28 |
| First Page: | 3303 |
| Last Page: | 3322 |
| DOI: | https://doi.org/10.1016/j.tcs.2011.03.018 |
| Institutes: | Fakultät für Angewandte Informatik |
| Fakultät für Angewandte Informatik / Institut für Informatik | |
| Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
| Licence (German): |  CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand) |
