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• W307324957 abstract "We construct pseudorandom generators for combinatorial shapes, which substantially generalize combinatorial rectangles, $epsilon$-biased spaces, 0/1 halfspaces, and 0/1 modular sums. A function $f:[m]^nrightarrow{0,1}$ is an $(m,n)$-combinatorial shape if there exist sets $A_1,ldots,A_nsubseteq[m]$ and a symmetric function $h:{0,1}^nrightarrow{0,1}$ such that $f(x_1,ldots,x_n)=h(1_{A_1}(x_1),ldots,1_{A_n}(x_n))$. Our generator uses seed-length $O(log m+log n+log^2(1/varepsilon))$ to get error $varepsilon$. When $m=2$, this gives the first generator of seed-length $O(log n)$ that fools all weight-based tests, meaning that the distribution of the weight of any subset is $varepsilon$-close to the appropriate binomial distribution in statistical distance. Along the way, we give a generator for combinatorial rectangles with seed-length $O(log^{3/2}n)$ and error $1/mathrm{poly}(n)$, matching Lu's bound from ICALP 1998. For our proof we give a simple lemma which allows us to convert closene..." @default.
• W307324957 created "2016-06-24" @default.
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• W307324957 date "2010-01-01" @default.
• W307324957 modified "2023-09-23" @default.
• W307324957 title "Pseudorandom Generators for Combinatorial Shapes." @default.
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