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Average-Case Rigidity Lower Bounds
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DOI：10.1007/s00224-026-10268-9.png)
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Abstract
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It is shown that there exists f: {0,1)(n/2)& times; {0, 1)(n/2) -> {0, 1) in E(NP )such that for every 2(n/2 )& times; 2(n/2) matrix M of rank <= rho we have P-x,P- y[ f (x, y) not equal M-x,M- y] >= 1/2 - 2(-Omega(k)), whenever log rho <= delta n/k(logn+k) for a sufficiently small delta > 0, and n is large enough. This generalizes recent results which bound below the probability by 1/2 - Omega(1) or to constant circuits.
Keywords:
Average-case lower bounds
Matrix rigidity
Correlation bounds
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