Matrix Rigidity of Random Toeplitz Matrices

Computational Complexity, Volume 27, Issue 2, 2018, Pages 305-350.

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Keywords:
Matrix rigidity multi-linear functions multi-linear circuits 68Q17

Abstract:

We prove that random n -by- n Toeplitz (alternatively Hankel) matrices over F 2 have rigidity Ω( n 3 / r 2 log n ) for rank r ≥ √ n , with high probability. For r = o ( n /log n · loglog n ), this improves over the Ω( n 2 / r · log( n / r )) bound that is known for many explicit matrices. Our result implies that the explici...More

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