\newcommand{\etalchar}[1]{$^{#1}$}
\def\cprime{$'$}
\begin{thebibliography}{GMR{\etalchar{+}}12}

\bibitem[Ajt83]{Ajt83}
Mikl{\'o}s Ajtai.
\newblock {$\Sigma \sp{1}\sb{1}$}-formulae on finite structures.
\newblock {\em Annals of Pure and Applied Logic}, 24(1):1--48, 1983.

\bibitem[Amb05]{Ambainis05}
Andris Ambainis.
\newblock Polynomial degree and lower bounds in quantum complexity: Collision
  and element distinctness with small range.
\newblock {\em Theory of Computing}, 1(1):37--46, 2005.

\bibitem[AS04]{AaronsonS04}
Scott Aaronson and Yaoyun Shi.
\newblock Quantum lower bounds for the collision and the element distinctness
  problems.
\newblock {\em J.~of the ACM}, 51(4):595--605, 2004.

\bibitem[Aus16]{Austin2016}
Tim Austin.
\newblock Ajtai-{S}zemer\'edi theorems over quasirandom groups.
\newblock In {\em Recent trends in combinatorics}, volume 159 of {\em IMA Vol.
  Math. Appl.}, pages 453--484. Springer, [Cham], 2016.

\bibitem[AW89]{AjtaiW89}
Miklos Ajtai and Avi Wigderson.
\newblock Deterministic simulation of probabilistic constant-depth circuits.
\newblock {\em Advances in Computing Research - Randomness and Computation},
  5:199--223, 1989.

\bibitem[Bar89]{Barrington89}
David A.~Mix Barrington.
\newblock Bounded-width polynomial-size branching programs recognize exactly
  those languages in {NC}$^1$.
\newblock {\em J.~of Computer and System Sciences}, 38(1):150--164, 1989.

\bibitem[Baz09]{Bazzi09}
Louay M.~J. Bazzi.
\newblock Polylogarithmic independence can fool {DNF} formulas.
\newblock {\em SIAM J. Comput.}, 38(6):2220--2272, 2009.

\bibitem[BCK{\etalchar{+}}14]{BuhrmanCKLS14}
Harry Buhrman, Richard Cleve, Michal Kouck{\'{y}}, Bruno Loff, and Florian
  Speelman.
\newblock Computing with a full memory: catalytic space.
\newblock In {\em ACM Symp.~on the Theory of Computing (STOC)}, pages 857--866,
  2014.

\bibitem[BDPW10]{BeameDPW10}
Paul Beame, Matei David, Toniann Pitassi, and Philipp Woelfel.
\newblock Separating deterministic from randomized multiparty communication
  complexity.
\newblock {\em Theory of Computing}, 6(1):201--225, 2010.

\bibitem[BF92]{BabaiF92}
L{\'a}szl{\'o} Babai and Peter Frankl.
\newblock {\em Linear algebra methods in combinatorics}.
\newblock 1992.

\bibitem[BKT17]{BunKT17}
Mark Bun, Robin Kothari, and Justin Thaler.
\newblock The polynomial method strikes back: Tight quantum query bounds via
  dual polynomials.
\newblock {\em CoRR}, arXiv:1710.09079, 2017.

\bibitem[BNP08]{BabaiNP08}
L{\'a}szl{\'o} Babai, Nikolay Nikolov, and L{\'a}szl{\'o} Pyber.
\newblock Product growth and mixing in finite groups.
\newblock In {\em ACM-SIAM Symp.~on Discrete Algorithms (SODA)}, pages
  248--257, 2008.

\bibitem[Bra10]{Braverman10}
Mark Braverman.
\newblock Polylogarithmic independence fools {AC}$^{\mbox{0}}$ circuits.
\newblock {\em J.~of the ACM}, 57(5), 2010.

\bibitem[BT17]{BunT17}
Mark Bun and Justin Thaler.
\newblock A nearly optimal lower bound on the approximate degree of {AC0}.
\newblock {\em CoRR}, abs/1703.05784, 2017.

\bibitem[EGL{\etalchar{+}}92]{EvenGLNV92}
Guy Even, Oded Goldreich, Michael Luby, Noam Nisan, and Boban Velickovic.
\newblock Approximations of general independent distributions.
\newblock In {\em ACM Symp.~on the Theory of Computing (STOC)}, pages 10--16,
  1992.

\bibitem[FSS84]{FSS84}
Merrick~L. Furst, James~B. Saxe, and Michael Sipser.
\newblock Parity, circuits, and the polynomial-time hierarchy.
\newblock {\em Mathematical Systems Theory}, 17(1):13--27, 1984.

\bibitem[GLS12]{GavinskyLS12}
Dmitry Gavinsky, Shachar Lovett, and Srikanth Srinivasan.
\newblock Pseudorandom generators for read-once acc{\^{}}0.
\newblock In {\em IEEE Conf.~on Computational Complexity (CCC)}, pages
  287--297, 2012.

\bibitem[GMR{\etalchar{+}}12]{GopalanMRTV12}
Parikshit Gopalan, Raghu Meka, Omer Reingold, Luca Trevisan, and Salil Vadhan.
\newblock Better pseudorandom generators from milder pseudorandom restrictions.
\newblock In {\em IEEE Symp.~on Foundations of Computer Science (FOCS)}, 2012.

\bibitem[Gow08]{Gowers08}
W.~T. Gowers.
\newblock Quasirandom groups.
\newblock {\em Combinatorics, Probability {\&} Computing}, 17(3):363--387,
  2008.

\bibitem[Gre05a]{Green-supplement}
Ben Green.
\newblock An argument of {S}hkredov in the finite field setting, 2005.
\newblock Available at people.maths.ox.ac.uk/greenbj/papers/corners.pdf.

\bibitem[Gre05b]{Gre04-finite}
Ben Green.
\newblock Finite field models in additive combinatorics.
\newblock {\em Surveys in Combinatorics, London Math. Soc. Lecture Notes 327,
  1-27}, 2005.

\bibitem[H{\r{a}}s87]{Has87}
Johan H{\r{a}}stad.
\newblock {\em Computational limitations of small-depth circuits}.
\newblock MIT Press, 1987.

\bibitem[H{\aa}s14]{Hastad14a}
Johan H{\aa}stad.
\newblock On the correlation of parity and small-depth circuits.
\newblock {\em SIAM J.~on Computing}, 43(5):1699--1708, 2014.

\bibitem[IMP12]{ImpagliazzoMP-AC0-sat}
Russell Impagliazzo, William Matthews, and Ramamohan Paturi.
\newblock A satisfiability algorithm for {AC}$^{\mbox{0}}$.
\newblock In {\em ACM-SIAM Symp.~on Discrete Algorithms (SODA)}, pages
  961--972, 2012.

\bibitem[LMN93]{LMN93}
Nathan Linial, Yishay Mansour, and Noam Nisan.
\newblock Constant depth circuits, {F}ourier transform, and learnability.
\newblock {\em J.~of the ACM}, 40(3):607--620, 1993.

\bibitem[LN90]{LinialN90}
Nathan Linial and Noam Nisan.
\newblock Approximate inclusion-exclusion.
\newblock {\em Combinatorica}, 10(4):349--365, 1990.

\bibitem[Nis91]{Nis91}
Noam Nisan.
\newblock Pseudorandom bits for constant depth circuits.
\newblock {\em Combinatorica. An Journal on Combinatorics and the Theory of
  Computing}, 11(1):63--70, 1991.

\bibitem[Nis92]{Nis92}
Noam Nisan.
\newblock Pseudorandom generators for space-bounded computation.
\newblock {\em Combinatorica}, 12(4):449--461, 1992.

\bibitem[NN90]{NaN90}
J.~Naor and M.~Naor.
\newblock Small-bias probability spaces: efficient constructions and
  applications.
\newblock In {\em 22nd ACM Symp.~on the Theory of Computing (STOC)}, pages
  213--223. ACM, 1990.

\bibitem[Raz87]{Raz87}
Alexander Razborov.
\newblock Lower bounds on the dimension of schemes of bounded depth in a
  complete basis containing the logical addition function.
\newblock {\em Akademiya Nauk SSSR. Matematicheskie Zametki}, 41(4):598--607,
  1987.
\newblock English translation in Mathematical Notes of the Academy of Sci. of
  the USSR, 41(4):333-338, 1987.

\bibitem[Raz09]{Razborov09}
Alexander~A. Razborov.
\newblock A simple proof of {B}azzi's theorem.
\newblock {\em ACM Transactions on Computation Theory (TOCT)}, 1(1), 2009.

\bibitem[Sie04]{Siegel04}
Alan Siegel.
\newblock On universal classes of extremely random constant-time hash
  functions.
\newblock {\em SIAM J.~on Computing}, 33(3):505--543, 2004.

\bibitem[Ta{-}17]{Ta-Shma17}
Amnon Ta{-}Shma.
\newblock Explicit, almost optimal, epsilon-balanced codes.
\newblock In {\em ACM Symp.~on the Theory of Computing (STOC)}, pages 238--251,
  2017.

\bibitem[Tal17]{Tal17}
Avishay Tal.
\newblock Tight bounds on the fourier spectrum of {AC0}.
\newblock In {\em Conf.~on Computational Complexity (CCC)}, pages 15:1--15:31,
  2017.

\end{thebibliography}
