Kronecker products, low-depth circuits, and matrix rigidity

  title={Kronecker products, low-depth circuits, and matrix rigidity},
  author={Josh Alman},
  journal={Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing},
  • Josh Alman
  • Published 24 February 2021
  • Mathematics
  • Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
For a matrix M and a positive integer r, the rank r rigidity of M is the smallest number of entries of M which one must change to make its rank at most r. There are many known applications of rigidity lower bounds to a variety of areas in complexity theory, but fewer known applications of rigidity upper bounds. In this paper, we use rigidity upper bounds to prove new upper bounds in a few different models of computation. Our results include: - For any d>1, and over any field F, the N × N Walsh… 
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