Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > FOURIER SPECTRUM:
Reports tagged with Fourier spectrum:
TR01-006 | 18th October 2000
Rocco Servedio

#### On Learning Monotone DNF under Product Distributions

We show that the class of monotone $2^{O(\sqrt{\log n})}$-term DNF
formulae can be PAC learned in polynomial time under the uniform
distribution. This is an exponential improvement over previous
algorithms in this model, which could learn monotone
$o(\log^2 n)$-term DNF, and is the first efficient algorithm
for ... more >>>

TR12-063 | 17th May 2012
Raghav Kulkarni, Miklos Santha

#### Query complexity of matroids

Let $\mathcal{M}$ be a bridgeless matroid on ground set $\{1,\ldots, n\}$ and $f_{\mathcal{M}}: \{0,1\}^n \to \{0, 1\}$ be the indicator function of its independent sets. A folklore fact is that $f_\mathcal{M}$ is evasive," i.e., $D(f_\mathcal{M}) = n$ where $D(f)$ denotes the deterministic decision tree complexity of $f.$ Here we prove ... more >>>

TR19-017 | 6th February 2019
Chin Ho Lee

#### Fourier bounds and pseudorandom generators for product tests

We study the Fourier spectrum of functions $f\colon \{0,1\}^{mk} \to \{-1,0,1\}$ which can be written as a product of $k$ Boolean functions $f_i$ on disjoint $m$-bit inputs. We prove that for every positive integer $d$,
$\sum_{S \subseteq [mk]: |S|=d} |\hat{f_S}| = O(m)^d .$
Our upper bound ... more >>>

ISSN 1433-8092 | Imprint