Barmpalias, George and LewisPye, Andrew (2017) Differences of halting probabilities. Journal of Computer and System Sciences, 89. pp. 349360. ISSN 00220000

Text
 Accepted Version
Download (598kB)  Preview 
Abstract
We study the differences of MartinLöf random leftc.e. reals and show that for each pair of such reals α,β there exists a unique number r>0 such that qα−β is a MartinLöf random leftc.e. real for each positive rational q>r and a MartinLöf random rightc.e. real for each positive rational q<r. Based on this result we develop a theory of differences of halting probabilities, which answers a number of questions about MartinLöf random leftc.e. reals, including one of the few remaining open problems from the list of open questions in algorithmic randomness [21]. The halting probability of a prefixfree machine M restricted to a set X is the probability that the machine halts and outputs an element of X . Becher, Figueira, Grigorieff, and Miller asked whether ΩU(X) is MartinLöf random when U is universal and X is a View the MathML source set. We apply our theory of differences of halting probabilities to give a positive answer.
Item Type:  Article 

Official URL:  https://www.journals.elsevier.com/journalofcompu... 
Additional Information:  © 2017 Elsevier Inc. 
Divisions:  Mathematics 
Subjects:  Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Sets:  Departments > Mathematics 
Date Deposited:  20 Jun 2017 13:28 
Last Modified:  20 Mar 2019 03:15 
URI:  http://eprints.lse.ac.uk/id/eprint/81819 
Actions (login required)
View Item 