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 ...