[1]   Adi Akavia, Andrej Bogdanov, Siyao Guo, Akshay Kamath, and Alon Rosen: Candidate weak pseudorandom functions in AC⁰ ∘ MOD₂. In Proc. 5th Innovations in Theoret. Comp. Sci. Conf. (ITCS’14), pp. 251–260. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2014. [doi:10.1145/2554797.2554821]

[2]   Noga Alon and Ravi B Boppana: The monotone circuit complexity of Boolean functions. Combinatorica, 7(1):1–22, 1987. [doi:10.1007/BF02579196]

[3]   Alexander E Andreev: A method for obtaining efficient lower bounds for monotone complexity. Algebra and Logic, 26(1):1–18, 1987. Preliminary version in Doklady 282, 1985, pp.1033-1037. Original article in Algebra i Logika 26(1) 3–26, 1987 (Russian). [doi:10.1007/BF01978380]

[4]   Christer Berg and Staffan Ulfberg: Symmetric approximation arguments for monotone lower bounds without sunflowers. Comput. Complexity, 8(1):1–20, 1999. [doi:10.1007/s000370050017]

[5]   Eric Blais, Clément L. Canonne, Igor Carboni Oliveira, Rocco A. Servedio, and Li-Yang Tan: Learning circuits with few negations. In Proc. 18th Internat. Workshop on Approximation Algorithms for Combinat. Opt. Probl. (APPROX’15), pp. 512–527. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2015. [doi:10.4230/LIPIcs.APPROX-RANDOM.2015.512]

[6]   Avrim Blum, Carl Burch, and John Langford: On learning monotone Boolean functions. In Proc. 39th FOCS, pp. 408–415. IEEE Comp. Soc., 1998. [doi:10.1109/SFCS.1998.743491]

[7]   Andrej Bogdanov and Alon Rosen: Pseudorandom functions: Three decades later. In Yehuda Lindell, editor, Tutorials on the Foundations of Cryptography, pp. 79–158. Springer, 2017. [doi:10.1007/978-3-319-57048-8_3]

[8]   Clément L. Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, and Karl Wimmer: Testing k-monotonicity: The rise and fall of Boolean functions. Theory of Computing, 15(1):1–55, 2019. Preliminary version in ITCS’17. [doi:10.4086/toc.2019.v015a001]

[9]   Dana Dachman-Soled, Vitaly Feldman, Li-Yang Tan, Andrew Wan, and Karl Wimmer: Approximate resilience, monotonicity, and the complexity of agnostic learning. In Proc. 26th Ann. ACM–SIAM Symp. on Discrete Algorithms (SODA’15), pp. 498–511. SIAM, 2015. [doi:10.1137/1.9781611973730.34]

[10]   Yuval Filmus: An orthogonal basis for functions over a slice of the Boolean hypercube. Electr. J. Combinat., 23(1):P1.23, 2016. [doi:10.37236/4567]

[11]   Yuval Filmus and Elchanan Mossel: Harmonicity and invariance on slices of the Boolean cube. In Proc. 31st Comput. Complexity Conf. (CCC’16), pp. 16:1–13. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2016. [doi:10.4230/LIPIcs.CCC.2016.16]

[12]   Oded Goldreich, Shafi Goldwasser, and Silvio Micali: How to construct random functions. J. ACM, 33(4):792–807, 1986. [doi:10.1145/6490.6503]

[13]   Elena Grigorescu, Akash Kumar, and Karl Wimmer: Flipping out with many flips: Hardness of testing k-monotonicity. SIAM J. Comput., 33(4):2111–2125, 2019. [doi:10.1137/18M1217978]

[14]   Siyao Guo and Ilan Komargodski: Negation-limited formulas. Theoret. Comput. Sci., 660:75–85, 2017. [doi:10.1016/j.tcs.2016.11.027]

[15]   Siyao Guo, Tal Malkin, Igor C Oliveira, and Alon Rosen: The power of negations in cryptography. In Proc. Theory of Cryptography Conf. (TCC’15), pp. 36–65. Springer, 2015. [doi:10.1007/978-3-662-46494-6_3]

[16]   Danny Harnik and Ran Raz: Higher lower bounds on monotone size. In Proc. 32nd STOC, pp. 378–387. ACM Press, 2000. [doi:10.1145/335305.335349]

[17]   Wassily Hoeffding: Probability inequalities for sums of bounded random variables. J. Amer. Statistical Assoc., 58(301):13–30, 1963. Also available in The Collected Works of Wassily Hoeffding, 1994, pp. 409–426, Springer and at JSTOR. See also Theorem 1 in Clayton Scott’s lecture notes, U. Michigan, 2014. [doi:10.1080/01621459.1963.10500830]

[18]   Chengyu Lin and Shengyu Zhang: Sensitivity conjecture and log-rank conjecture for functions with small alternating numbers. In Proc. 44th Internat. Colloq. on Automata, Languages, and Programming (ICALP’17), pp. 51:1–13. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2017. [doi:10.4230/LIPIcs.ICALP.2017.51]

[19]   Nathan Linial, Yishay Mansour, and Noam Nisan: Constant depth circuits, Fourier transform, and learnability. J. ACM, 40(3):607–620, 1993. [doi:10.1145/174130.174138]

[20]   Andrey A Markov: On the inversion complexity of a system of functions. J. ACM, 5(4):331–334, 1958. [doi:10.1145/320941.320945]

[21]   Ryan O’Donnell: Analysis of Boolean Functions. Cambridge Univ. Press, 2014. [doi:10.1017/CBO9781139814782, arXiv:2105.10386]

[22]   Ryan O’Donnell and Karl Wimmer: KKL, Kruskal-Katona, and monotone nets. SIAM J. Comput., 42(6):2375–2399, 2013. Preliminary version in FOCS’09. [doi:10.1137/100787325]

[23]   Alexander A Razborov: Lower bounds for the monotone complexity of some Boolean functions. Soviet Math. Doklady, 31:354–357, 1985. Russian original at Mathnet.ru.

[24]   Benjamin Rossman: Correlation bounds against monotone NC¹. In Proc. 30th Comput. Complexity Conf. (CCC’15), pp. 392–411. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2015. [doi:10.4230/LIPIcs.CCC.2015.392]

[25]   Murali K Srinivasan: Symmetric chains, Gelfand–Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme. J. Algebraic Combinatorics, 34(2):301–322, 2011. [doi:10.1007/s10801-010-0272-2]

[26]   Éva Tardos: The gap between monotone and non-monotone circuit complexity is exponential. Combinatorica, 8(1):141–142, 1988. [doi:10.1007/BF02122563]