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Journal of the ACM
In this paper, Boolean functions in ,4C0 are studied using harmonic analysis on the cube. The main result is that an ACO Boolean function has almost all of its "power spectrum" on the low-order coefficients. An important ingredient of the proof is Hastad's switching lemma . This result implies several new properties of functions in -4C[': Functions in AC() have low "average sensitivity;" they may be approximated well by a real polynomial of low degree and they cannot be pseudorandom functiondoi:10.1145/174130.174138 fatcat:iwwlqkfxazgijjobyhhevsk4su