Fourier analysis of Boolean functions yields two phenomena—preservation of coordinate influence under random 2-to-1 minors and sharp thresholds—that classify hardness and tractability for Boolean PCSP minions of unate or polynomial threshold functions, extending prior ordered-PCSP results.
A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions
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Boolean PCSPs through the lens of Fourier Analysis
Fourier analysis of Boolean functions yields two phenomena—preservation of coordinate influence under random 2-to-1 minors and sharp thresholds—that classify hardness and tractability for Boolean PCSP minions of unate or polynomial threshold functions, extending prior ordered-PCSP results.