Computable Randomness, and Coding the Orbits of the Collatz Map

Graduate Thesis Or Dissertation

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/cn69m8939

Descriptions

Attribute Name	Values
Creator	Robson, Charlie
Abstract	In this thesis I will look at a definition of computable randomness from Algorithmic Information Theory as defined by Andre Nies through the lens of Computable Analaysis asdefined by Klaus Weihrauch. I will show that despite the fact that these two paradigmsgenerate distinct classes of computable supermartingales, the class of sets on which nocomputable supermartingale succeeds of either type is identical. Therefore, both theoriesgenerate the same collection of computably random sets. I will then consider how onemight apply some of the techniques in Algorithmic Information Theory, including prefixfree codes and the Kraft Inequality, to the study of the Collatz Conjecture. Keywords: Collatz Conjecture, Computability, Algorithmic Randomness, Computable Analysis, Complexity
License	All rights reserved
Resource Type	Dissertation
Date Available	2017-06-28T20:58:29+00:00
Date Issued	2017-06-15
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2018
Advisor	Ren, Guo
Committee Member	Thomann, Enrique Koslicki, David Cotilla-Sanchez, Eduardo Zhang, Eugene
Academic Affiliation	Mathematics
Non-Academic Affiliation	Oregon State University. Graduate School
Déclaration de droits	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Replaces	http://hdl.handle.net/1957/61676

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