Polynomial-clone reducibility
Date
2010
Authors
Contributor
Advisor
Department
Instructor
Depositor
Speaker
Researcher
Consultant
Interviewer
Narrator
Transcriber
Annotator
Journal Title
Journal ISSN
Volume Title
Publisher
University of Hawaii at Manoa
Volume
Number/Issue
Starting Page
Ending Page
Alternative Title
Abstract
Polynomial-clone reducibilities are generalizations of the truth-table reducibilities. A polynomial clone is a set of functions over a finite set X that is closed under composition and contains all the constant and projection functions. For a fixed polynomial clone C, a sequence B ∈ X ω is C-reducible to A ∈ X ω if there is an algorithm that computes B from A using only effectively selected functions from C. We show that if A is a Kurtz random sequence and C1 C2 are distinct polynomial clones, then there is a sequence B that is C1 -reducible to A but not C2 -reducible to A. This implies a generalization of a result first proved by Lachlan for the case |X| = 2. We also show that the same result holds if Kurtz random is replaced by Kolmogorov-Loveland stochastic.
Description
Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2010
Keywords
Citation
Extent
28 pages
Format
Geographic Location
Time Period
Related To
Related To (URI)
Table of Contents
Rights
All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Rights Holder
Local Contexts
Collections
Email libraryada-l@lists.hawaii.edu if you need this content in ADA-compliant format.