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 spa...

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Bibliographic Details
Published in:Theory of computing systems Vol. 59; no. 1; pp. 99 - 111
Main Authors: Devadas, Sheela, Rubinfeld, Ronitt
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2016
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Homomorphisms
Integer programming
Integers
Mathematical analysis
Mathematical models
Proving
Queries
Studies
Theory of Computation
Vector space
Vector spaces
Linearity testing
Property testing
ISSN:1432-4350, 1433-0490
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.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-015-9639-z