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computational complexity

, Volume 24, Issue 4, pp 851–879 | Cite as

On Rigid Matrices and U-Polynomials

  • Noga Alon
  • Gil CohenEmail author
Article
  • 74 Downloads

Abstract

We introduce a class of polynomials, which we call U-polynomials, and show that the problem of explicitly constructing a rigid matrix can be reduced to the problem of explicitly constructing a small hitting set for this class. We prove that small-bias sets are hitting sets for the class of U-polynomials, though their size is larger than desired. Furthermore, we give two alternative proofs for the fact that small-bias sets induce rigid matrices.

Finally, we construct rigid matrices from unbalanced expanders, with essentially the same size as the construction via small-bias sets.

Keywords

Matrix rigidity small-bias sets unbalanced expanders 

Subject classification

68Q17 68R05 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Sackler School of Mathematics and Blavatnik School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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