Barmpalias, George, Fang, Nan and LewisPye, Andrew (2016) Optimal asymptotic bounds on the oracle use in computations from Chaitin’s Omega. Journal of Computer and System Sciences, 82 (8). pp. 12831299. ISSN 00220000

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Abstract
Chaitin’s number is the halting probability of a universal prefixfree machine, and although it depends on the underlying enumeration of prefixfree machines, it is always Turingcomplete. It can be observed, in fact, that for every computably enumerable (c.e.) real �, there exists a Turing functional via which computes �, and such that the number of bits of that are needed for the computation of the first n bits of � (i.e. the use on argument n) is bounded above by a computable function h(n) = n + o (n). We characterise the asymptotic upper bounds on the use of Chaitin’s in oracle computations of halting probabilities (i.e. c.e. reals). We show that the following two conditions are equivalent for any computable function h such that h(n)P
Item Type:  Article 

Official URL:  http://www.journals.elsevier.com/journalofcomput... 
Additional Information:  © 2016 Elsevier 
Divisions:  Mathematics 
Subjects:  Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Sets:  Departments > Mathematics 
Date Deposited:  17 May 2016 15:07 
Last Modified:  20 Jul 2019 02:15 
Projects:  2010Y2GB03, 2014CB340302 
Funders:  Chinese Government, Chinese Academy of Sciences, China Basic Research Program 
URI:  http://eprints.lse.ac.uk/id/eprint/66539 
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