Graduate Thesis Or Dissertation

 

Computable Randomness, and Coding the Orbits of the Collatz Map Public Deposited

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  • 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.
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  • description.provenance : Submitted by Charles Robson (robsonc@oregonstate.edu) on 2017-06-18T22:13:15ZNo. of bitstreams: 2license_rdf: 1370 bytes, checksum: cd1af5ab51bcc7a5280cf305303530e9 (MD5)RobsonCharlieD2018.pdf: 549346 bytes, checksum: 5842b3de51c9dd9264bac50a0ab25721 (MD5)
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