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Electronic Colloquium on Computational Complexity

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TR22-132 | 18th September 2022
Harm Derksen, Emanuele Viola

Fooling polynomials using invariant theory

We revisit the problem of constructing explicit pseudorandom generators
that fool with error $\epsilon$ degree-$d$ polynomials in $n$ variables
over the field $F_q$, in the case of large $q$. Previous constructions
either have seed length at least $2^{d}\log q$, and thus are only non-trivial
when the degree is less than ... more >>>


TR22-131 | 18th September 2022
Rafael Mendes de Oliveira, Akash Sengupta

Radical Sylvester-Gallai for Cubics

Let $\mathcal{F} = \{F_1, \ldots, F_m\}$ be a finite set of irreducible homogeneous multivariate polynomials of degree at most $3$ such that $F_i$ does not divide $F_j$ for $i\neq j$.
We say that $\mathcal{F}$ is a cubic radical Sylvester-Gallai configuration if for any two distinct $F_i,F_j$ there exists a ... more >>>


TR22-130 | 15th September 2022
Hamed Hatami, Kaave Hosseini, Xiang Meng

A Borsuk-Ulam lower bound for sign-rank and its application

We introduce a new topological argument based on the Borsuk-Ulam theorem to prove a lower bound on sign-rank.

This result implies the strongest possible separation between randomized and unbounded-error communication complexity. More precisely, we show that for a particular range of parameters, the randomized communication complexity of ... more >>>



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