Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > NUMBER-ON-THE-FOREHEAD MODEL:
TR16-138 | 3rd September 2016
Alexander A. Sherstov

#### On multiparty communication with large versus unbounded error

The communication complexity of $F$ with unbounded error is the limit of the $\epsilon$-error randomized complexity of $F$ as $\epsilon\to1/2.$ Communication complexity with weakly bounded error is defined similarly but with an additive penalty term that depends on $1/2-\epsilon$. Explicit functions are known whose two-party communication complexity with unbounded error ... more >>>

TR22-123 | 4th September 2022
Alexander A. Sherstov

#### The Approximate Degree of DNF and CNF Formulas

The approximate degree of a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is the minimum degree of a real polynomial $p$ that approximates $f$ pointwise: $|f(x)-p(x)|\leq1/3$ for all $x\in\{0,1\}^n.$ For every $\delta>0,$ we construct CNF and DNF formulas of polynomial size with approximate degree $\Omega(n^{1-\delta}),$ essentially matching the trivial upper bound of $n.$ This ... more >>>

ISSN 1433-8092 | Imprint