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On Matrix Multiplication and Polynomial Identity Testing
[article]

2022
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arXiv
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pre-print

We show that lower bounds on the border rank of matrix multiplication can be used to non-trivially derandomize polynomial identity testing for small algebraic circuits. Letting R(n) denote the border rank of n × n × n matrix multiplication, we construct a hitting set generator with seed length O(√(n)·R^-1(s)) that hits n-variate circuits of multiplicative complexity s. If the matrix multiplication exponent ω is not 2, our generator has seed length O(n^1 - ε) and hits circuits of size O(n^1 + δ)

arXiv:2208.01078v1
fatcat:676drnxzmvduhnk5takbdztiqm