# Query-efficient algorithms for polynomial interpolation over composites

@article{Gopalan2006QueryefficientAF,
title={Query-efficient algorithms for polynomial interpolation over composites},
author={Parikshit Gopalan},
journal={SIAM J. Comput.},
year={2006},
volume={38},
pages={1033-1057}
}
• P. Gopalan
• Published 22 January 2006
• Computer Science
• SIAM J. Comput.
The problem of polynomial interpolation is to reconstruct a polynomial based on its valuations on a set of inputs <i>I</i>. We consider the problem over <i>Z</i><inf>m</inf> when <i>m</i> is composite. We ask the question: Given I ⊆ <i>Z</i><inf>m</inf>, how many evaluations of a polynomial at points in I are required to compute its value at every point in I? Surprisingly for composite <i>m</i>, this number can vary exponentially between log[<i>I</i>] and [<i>I</i>] in contrast to the prime…
Polynomial approximations over Z / p k Z
We study approximation of Boolean functions by low-degree polynomials over the ring Z/pkZ. More precisely, given a Boolean function F : {0, 1}n → {0, 1}, define its k-lift to be Fk : {0, 1}n → {0,
Computing with polynomials over composites
• Computer Science, Mathematics
• 2006
This thesis addresses some such prime vs. composite problems from algorithms, complexity and combinatorics, and the surprising connections between them, and shows that symmetric polynomials can viewed as simultaneous communication protocols.
Constructing Ramsey graphs from Boolean function representations
• P. Gopalan
• Mathematics, Computer Science
21st Annual IEEE Conference on Computational Complexity (CCC'06)
• 2006
The barrier to better Ramsey constructions through such algebraic methods appears to be the construction of lower degree representations, and it is shown that better bounds cannot be obtained using symmetric polynomials.
On polynomial approximations over Z/2kZ
• Mathematics, Computer Science
STACS
• 2017
It is observed that the model the authors study subsumes the model of non-classical polynomials in the sense that proving bounds in the model implies bounds on the agreement ofNon- classical poynomials with Boolean functions.
Towards understanding the approximation of Boolean functions by nonclassical polynomials
The ability of nonclassical polynomials to approximate Boolean functions with respect to both previously studied and new notions of approximation is investigated.
Polynomial Interpolation over the Residue Rings Zn
• Mathematics
• 2015
We consider the problem of polynomial interpolation over the residue rings Zn. The general case can easily be reduced to the case of n = pk due to the Chinese reminder theorem. In contrast to the