Tight Lower Bounds for Testing Linear Isomorphism

  title={Tight Lower Bounds for Testing Linear Isomorphism},
  author={Elena Grigorescu and Karl Wimmer and Ning Xie},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
We study lower bounds for testing membership in families of linear/affine-invariant Boolean functions over the hypercube. A family of functions P ⊆ {{0, 1} → {0, 1}} is linear/affine invariant if for any f ∈ P , it is the case that f ◦L ∈ P for any linear/affine transformation L of the domain. Motivated by the recent resurgence of attention to the permutation isomorphism problem, we first focus on families that are linearly/affinely isomorphic to some fixed function. A function f : {0, 1} → {0… CONTINUE READING