Lecture 6 — April 14 , 2017
نویسنده
چکیده
A zero sum game is a simultaneous move game between 2 players. Such a game is represented by a matrix A ∈ Rm×n. The strategies of the “row” (resp. “column”) player are the rows (resp. columns) of A. If the row player plays strategy i ∈ [m] and the column player plays j ∈ [n] then the outcome is Aij . 1 Interpret this as that the row player pays Aij amount of money to the column player, therefore the row player tries to minimize Aij while the column player tries to maximize it.
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Lecture 12 : April 13 , 2017
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 ...
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