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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/103636 https://orcid.org/0000-0001-8253-7714 https://orcid.org/0000-0002-4353-7639 |
| 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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