Barmpalias, George, Lewis-Pye, Andy and Teutsch, Jason (2016) Lower bounds on the redundancy in computations from random oracles via betting strategies with restricted wagers. Information and Computation, 251 . ISSN 0890-5401
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Abstract
The Kuˇcera-Gács theorem [Kuˇc85, Gác86] is a landmark result in algorithmic randomness asserting that every real is computable from a Martin-Löf random real. If the computation of the first n bits of a sequence requires n + h(n) bits of the random oracle, then h is the redundancy of the computation. Kuˇcera implicitly achieved redundancy n log n while Gács used a more elaborate coding procedure which achieves redundancy p n log n. A similar bound is implicit in the later proof by Merkle and Mihailovi´c [MM04]. In this paper we obtain optimal strict lower bounds on the redundancy in computations from Martin-Löf random oracles. We show that any nondecreasing computable function g such that P n 2
| Item Type: | Article | |||||||||
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| Official URL: | http://www.journals.elsevier.com/information-and-c... | |||||||||
| Additional Information: | © 2016 Elsevier | |||||||||
| Library of Congress subject classification: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
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| Sets: | Departments > Mathematics | |||||||||
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| Date Deposited: | 26 Sep 2016 16:15 | |||||||||
| URL: | http://eprints.lse.ac.uk/67867/ |
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