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Electronic Colloquium on Computational Complexity

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All reports by Author Yuval Filmus:

TR21-093 | 1st July 2021
Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, Akshayaram Srinivasan

Bounded Indistinguishability for Simple Sources

Revisions: 1

A pair of sources $\mathbf{X},\mathbf{Y}$ over $\{0,1\}^n$ are $k$-indistinguishable if their projections to any $k$ coordinates are identically distributed. Can some $\mathit{AC^0}$ function distinguish between two such sources when $k$ is big, say $k=n^{0.1}$? Braverman's theorem (Commun. ACM 2011) implies a negative answer when $\mathbf{X}$ is uniform, whereas Bogdanov et ... more >>>

TR20-180 | 2nd December 2020
Yuval Filmus, Or Meir, Avishay Tal

Shrinkage under Random Projections, and Cubic Formula Lower Bounds for $\mathbf{AC}^0$

Revisions: 3

HÃ¥stad 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 >>>

TR19-029 | 20th February 2019
Yuval Filmus, Lianna Hambardzumyan, Hamed Hatami, Pooya Hatami, David Zuckerman

Biasing Boolean Functions and Collective Coin-Flipping Protocols over Arbitrary Product Distributions

The seminal result of Kahn, Kalai and Linial shows that a coalition of $O(\frac{n}{\log n})$ players can bias the outcome of *any* Boolean function $\{0,1\}^n \to \{0,1\}$ with respect to the uniform measure. We extend their result to arbitrary product measures on $\{0,1\}^n$, by combining their argument with a completely ... more >>>

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