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Electronic Colloquium on Computational Complexity

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TR25-054 | 24th April 2025
Ronen Shaltiel

Extractors for Samplable Distribution with Polynomially Small Min-Entropy

Trevisan and Vadhan (FOCS 2000) introduced the notion of (seedless) extractors for samplable distributions. They showed that under a very strong complexity theoretic hardness assumption (specifically, that there exists a problem in $\E=\DTIME(2^{O(n)})$ that cannot be computed by size $2^{\Omega(n)}$ circuits that have an oracle to $\Sigma_6^{\P}$) there are extractors ... more >>>


TR25-053 | 23rd April 2025
Amir Shpilka

On Approximate Symmetric Polynomials and Tightness of Homogenization Results

Motivated by questions concerning the multilinear and homogeneous complexity of the elementary symmetric polynomials, we prove the following results:

We first show that by making small modifications to the nonzero coefficients of the degree-$K$, $N$-variate elementary symmetric polynomial $\sigma_{N,K}$, one obtains a polynomial that can be computed by a monotone ... more >>>


TR25-052 | 21st April 2025
Zeyu Guo, Siki Wang

Deterministic Depth-4 PIT and Normalization

Revisions: 1

In this paper, we initiate the study of deterministic PIT for $\Sigma^{[k]}\Pi\Sigma\Pi^{[\delta]}$ circuits over fields of any characteristic, where $k$ and $\delta$ are bounded. Our main result is a deterministic polynomial-time black-box PIT algorithm for $\Sigma^{[3]}\Pi\Sigma\Pi^{[\delta]}$ circuits, under the additional condition that one of the summands at the top $\Sigma$ ... more >>>



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