Isoperimetric inequalities for real‐valued functions with applications to monotonicity testing
Hadley Black,
Iden Kalemaj,
Sofya Raskhodnikova
Abstract:We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real‐valued functions . Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real‐valued function over an arbitrary partially ordered domain as a collection of Boolean functions over the same domain, roughly capturing the distance of to monotonicity and the structure of violations of to monotonicity. We apply our generali… Show more
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