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Algebraic property testing Elad Haramaty Northeastern University - PowerPoint PPT Presentation

Feb 27, 2024 •24 likes •64 views

Algebraic property testing Elad Haramaty Northeastern University Algebraic property testing Property testing : using O (1) queries determined with high probability if f is in the code or far from the code Algebraic codes : linear codes that are

  1. Algebraic property testing Elad Haramaty Northeastern University

  2. Algebraic property testing Property testing : using O (1) queries determined with high probability if f is in the code or far from the code Algebraic codes : linear codes that are affine invariant

  3. Algebraic property testing Example : low degree polynomials [RS96,ALMSS98,AS03, FS95,AKKLR05, KR06, JPRZ09, BKSSZ10, H SS11, H GS15] More examples : lifted codes (codes defined by their restriction on subspaces) [KS08, H RS13, H GS15] Applications : PCP [ALMSS92], Small sets expanders [BGHMRS12], Xor lemmas for polys [VW08], Algorithms [ABG H 14]

  4. More interesting problems - Interactive coding : transcript resilient to error - Natural communication : uncertainty, evolve - Protocols and algorithms : distributed and centralized Thanks!

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