Proving Properties of Fibonacci Representations via Automata Theory
| dc.contributor.author | Shan, Sonja Linghui | |
| dc.date.accessioned | 2024-01-22T15:14:48Z | |
| dc.date.available | 2024-01-22T15:14:48Z | |
| dc.date.issued | 2024-01-22 | |
| dc.date.submitted | 2024-01-10 | |
| dc.description.abstract | In this work, we introduce a novel framework for mechanically testing the completeness and unambiguity of Fibonacci-based representations via automata theory. We call a representation (or a number system) complete and unambiguous when it provides one and only one representation for each number in the range covered by the representation. Many commonly used representations are complete and unambiguous: consider the familiar binary number system—each natural number has a unique representation up to leading zeros. Additionally, if a representation is complete, we describe an algorithm, of O(log n) complexity, to find a representation for any particular number n. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/20258 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | automata theory | en |
| dc.subject | numeration systems | en |
| dc.subject | Fibonacci numbers | en |
| dc.title | Proving Properties of Fibonacci Representations via Automata Theory | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | David R. Cheriton School of Computer Science | en |
| uws-etd.degree.discipline | Computer Science | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Shallit, Jeffrey | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |