Lecture 12 : April 13 , 2017
نویسنده
چکیده
Last Time During the last lecture we completed an argument for a 2 1 d−1 ) lower bound for depth-d circuits for parity (PAR) using Hastad’s Switching Lemma [H̊as87], which stated that, for f : {0, 1} → {−1, 1}, if CNFwidth(f) = t, Pρ←Rp(DNFwidth(f ρ) = s) ≥ (7ps) We proved the Weak Switching Lemma, asserting a (40ps2) lower bound for this probability as opposed to the tighter bound given by the true Switching Lemma. The proof involved a discussion of s-clipped decision trees.
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