Campus Units
Computer Science, Mathematics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
2-11-2016
Journal or Book Title
Computability
Volume
5
Issue
1
First Page
13
Last Page
27
DOI
10.3233/COM-150035
Abstract
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.
Copyright Owner
IOS Press
Copyright Date
2016
Language
en
File Format
application/pdf
Recommended Citation
Hirschfeldt, Dennis R.; Jockusch, Carl G.; McNicholl, Timothy H.; and Schupp, Paul E., "Asymptotic density and the coarse computability bound" (2016). Mathematics Publications. 110.
https://lib.dr.iastate.edu/math_pubs/110
Comments
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." Computability 5, no. 1 (2016): 13-27, doi:10.3233/COM-150035. Posted with permission.