A Self-Tester for Linear Functions over the Integers with an Elementary Proof of Correctness

We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of self-testing to homomorphisms on a multidimensional vector spac...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Devadas, Sheela, Rubinfeld, Ronitt
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 22.06.2015
Subjects:	Algorithms Domains Homomorphisms Integers Linear functions Linearity Self testing Vector space
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of self-testing to homomorphisms on a multidimensional vector space. We show that our self-testing algorithm for the univariate case can be directly generalized to vector space domains. The number of queries made by our algorithms is independent of domain size.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1412.5484