Papers for

hardware circuit designers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Exponential correlation bounds limit polynomial approximations of xor majority functions

Exponential Correlation Bounds for Polynomials

Abstract: We prove that the XOR of $k$ majorities on disjoint blocks of $\ell$ bits has correlation at most $(2d/\sqrt{\ell})^k$ with every degree-$d$ polynomial over $\mathbb F_2$. By known techniques, this implies pseudorandom generators with polylogarithmic seed length for low-degree polynomials over $\mathbb F_2$ and for alternating circuits with parity gates.

Wed 23 SeptComputational Complexity

The gist

The paper shows that combining multiple majority votes on groups of bits using XOR produces a function that low-degree polynomials cannot closely mimic. The authors prove a strong upper bound on how similar these polynomials can be to such combined majority functions. This means the combined majority functions are very different from simple polynomial functions, making them useful to create sequences that look random to certain kinds of computations. The results help design tools that generate pseudorandom numbers with short starting information for use in complex circuit models and polynomial computations.

Open → 2609.28839v1