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Limits of the Kucera-Gacs coding method

Barmpalias, George and Lewis-Pye, Andrew (2017) Limits of the Kucera-Gacs coding method. In: Post-proceedings volume of SEALS 2016 (South Eastern Logic Symposium). World Scientific.

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Abstract

Every real is computable from a Martin-Loef random real. This well known result in algorithmic randomness was proved by Kucera and Gacs. In this survey article we discuss various approaches to the problem of coding an arbitrary real into a Martin-Loef random real,and also describe new results concerning optimal methods of coding. We start with a simple presentation of the original methods of Kucera and Gacs and then rigorously demonstrate their limitations in terms of the size of the redundancy in the codes that they produce. Armed with a deeper understanding of these methods, we then proceed to motivate and illustrate aspects of the new coding method that was recently introduced by Barmpalias and Lewis-Pye and which achieves optimal logarithmic redundancy, an exponential improvement over the original redundancy bounds.

Item Type: Book Section
Official URL: http://www.worldscientific.com/
Additional Information: © 2017 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Departments > Mathematics
Date Deposited: 06 Nov 2017 14:53
Last Modified: 21 Jun 2019 23:14
Projects: 2010Y2GB03, 2014CB340302.
Funders: Chinese Academy of Sciences (CAS) President’s International Fellowship Initiative, New Zealand and the China Basic Research Program (973)
URI: http://eprints.lse.ac.uk/id/eprint/85076

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