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

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
Main Authors: Devadas, Sheela (Author), Rubinfeld, Ronitt (Contributor), Devadas, Srinivas (Contributor)
Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Springer US, 2016-07-15T22:56:51Z.
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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.
National Science Foundation (U.S.) (grants CCF-1217423, CCF-1065125, and CCF-1420692)
Israel Science Foundation (grant 1536/14)

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