NDLI: A Unifying Approach to the Gamma Question

Content Provider	IEEE Xplore Digital Library
Author	Monin, B. Nies, A.
Copyright Year	2015
Description	Author affiliation: Univ. of Auckland, Auckland, New Zealand (Nies, A.) \|\| Victoria Univ. of Wellington, Wellington, New Zealand (Monin, B.)
Abstract	The Gamma question was formulated by Andrews et al. In "Asymptotic density, computable trace ability and 1-randomness" (2013, available at http://www.math.wisc.edu/~lempp/papers/traceable.pdf). It is related to the recent notion of coarse computability which stems from complexity theory. The Gamma value of an oracle set measures to what extent each set computable with the oracle is approximable, in the sense of density, by a computable set. The closer to 1 this value is, the closer the oracle is to being computable. The Gamma question asks whether this value can be strictly in between 0 and 1/2. We say that an oracle is weakly Schnorr engulfing if it computes a Schnorr test that succeeds on all computable reals. We show that each non weakly Schnorr engulfing oracle has a Gamma value of at least 1/2. Together with a recent result of Kjos-Hanssen, Stephan, and Terwijn, this establishes new examples of such oracles. We also give a unifying approach to oracles with Gamma value 0. We say that an oracle is infinitely often equal with bound h if it computes a function that agrees infinitely often with each computable function bounded by h. We show that every oracle which is infinitely equal with bound 2dn for d>1 has a Gamma value of 0. This provides new examples of such oracles as well. We present a combinatorial characterization of being weakly Schnorr engulfing via traces, which is inspired by the study of cardinal characteristics in set theory.
Starting Page	585
Ending Page	596
File Size	308395
Page Count	12
File Format	PDF
ISBN	9781479988754
ISSN	10436871
DOI	10.1109/LICS.2015.60
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-07-06
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Atomic measurements Complexity theory Random sequences Electronic mail Encoding Computer science Density measurement coarse computability Algorithmic randomness computability
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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