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TR08-012 | 20th November 2007 00:00
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#### A Note on the Distance to Monotonicity of Boolean Functions

**Abstract:**
Given a boolean function, let epsilon_M(f) denote the smallest distance between f and a monotone function on {0,1}^n. Let delta_M(f) denote the fraction of hypercube edges where f violates monotonicity. We give an alternative proof of the tight bound: delta_M(f) >= 2/n eps_M(f) for any boolean function f. This was already shown by Raskhodnikova earlier.