Asymptotic density and the coarse computability bound Hirschfeldt, Dennis Jockusch, Carl McNicholl, Timothy Schupp, Paul
dc.contributor.department Computer Science
dc.contributor.department Mathematics 2018-02-18T17:04:27.000 2020-06-30T05:59:37Z 2020-06-30T05:59:37Z Fri Jan 01 00:00:00 UTC 2016 2016-02-11
dc.description.abstract <p>For r is an element of [0, 1] we say that a set A subset of omega is coarsely computable at density r if there is a computable set C such that {n: C(n) = A(n)} has lower density at least r. Let gamma (A) = sup{r : A is coarsely computable at density r}. We study the interactions of these concepts with Turing reducibility. For example, we show that if r is an element of (0, 1] there are sets A(0), A(1) such that gamma(A(0)) = gamma(A(1)) = r where A(0) is coarsely computable at density r while A(1) is not coarsely computable at density r. We show that a real r is an element of [0, 1] is equal to gamma (A) for some c.e. set A if and only if r is left-Sigma(0)(3). A surprising result is that if G is a Delta(0)(2) 1-generic set, and A < = (T) G with gamma(A) = 1, then A is coarsely computable at density 1.</p>
dc.description.comments <p>This is a manuscript of an article published as Hirschfeldt, Denis R., Carl G. Jockusch Jr, Timothy H. McNicholl, and Paul E. Schupp. "Asymptotic density and the coarse computability bound." <em>Computability</em> 5, no. 1 (2016): 13-27, doi:<a href="" target="_blank">10.3233/COM-150035</a>. Posted with permission.</p>
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dc.identifier archive/
dc.identifier.articleid 1109
dc.identifier.contextkey 10462982
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/110
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 18:40:07 UTC 2022
dc.source.uri 10.3233/COM-150035
dc.subject.disciplines Applied Mathematics
dc.subject.disciplines Mathematics
dc.subject.disciplines Numerical Analysis and Computation
dc.subject.keywords Asymptotic density
dc.subject.keywords coarse computability
dc.subject.keywords Turing degrees
dc.title Asymptotic density and the coarse computability bound
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 52624580-cc7d-4600-800e-c84af32578ba
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relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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