Constrained codes have been used in data storage systems, such as magnetic tapes,
CD’s and DVD’s, in order to reduce the likelihood of errors by predictable noise.
The study of constrained codes is based on the study of sofic shifts, which are sets of
bi-infinite sequences that can be presented using labeled directed graphs called presentations. In this thesis, we will primarily focus on two classes of sofic shifts, namely shifts of finite type (SFT’s) and periodic-finite-type shifts (PFT’s), and examine their properties.
We first consider Shannon covers of sofic shifts. A Shannon cover of a sofic shift
is a deterministic presentation with the smallest number of vertices among all deterministic presentations of the shift. Indeed, a Shannon cover is used as a canonical presentation of a sofic shift, and furthermore, it is used when computing the capacity of the shift or when constructing a finite-state encoder. We follow an algorithm by Crochemore, Mignosi and Restivo which constructs a deterministic presentation of
an SFT and we see how to derive a Shannon cover from the presentation under their
algorithm. Furthermore, as a method to determine whether a given deterministic
presentation is a Shannon cover of a sofic shift, we will provide, based on research by
Jonoska, a sufficient condition for a given presentation to have the smallest number
of vertices among all presentations of the shift.
We then move our focus towards PFT’s, and investigate new properties of PFT’s from various perspectives. We define three types of periods that can be associated with a PFT and do pairwise comparisons between them. Also, we consider the zeta function of a PFT, which is a generating function for the number of periodic sequences in the PFT, and present a simple formula to compute the zeta function of a PFT. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-08-08 14:08:36.876
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/2584 |
| Date | 12 August 2009 |
| Creators | Manada, Akiko |
| Contributors | Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | 466455 bytes, application/pdf |
| Rights | This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner. |
| Relation | Canadian theses |
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