We prove a new derandomization of Håstad's switching lemma, showing how to efficiently generate restrictions satisfying the switching lemma for DNF or CNF formulas of size $m$ using only $\widetilde{O}(\log m)$ random bits. Derandomizations of the switching lemma have been useful in many works as a key building-block for constructing ... more >>>

Robust sunflowers are a generalization of combinatorial sunflowers that have applications in monotone circuit complexity, DNF sparsification, randomness extractors, and recent advances on the Erd\H{o}s-Rado sunflower conjecture. The recent breakthrough of Alweiss, Lovett, Wu and Zhang gives an improved bound on the maximum size of a $w$-set system that excludes ... more >>>

Håstad showed that any De Morgan formula (composed of AND, OR and NOT gates) shrinks by a factor of $O(p^{2})$ under a random restriction that leaves each variable alive independently with probability $p$ [SICOMP, 1998]. Using this result, he gave an $\widetilde{\Omega}(n^{3})$ formula size lower bound for the Andreev function, ... more >>>