Russell Impagliazzo, Valentine Kabanets

We give a simple combinatorial proof of the Chernoff-Hoeffding concentration bound~\cite{Chernoff, Hof63}, which says that the sum of independent $\{0,1\}$-valued random variables is highly concentrated around the expected value. Unlike the standard proofs,

our proof does not use the method of higher moments, but rather uses a simple ...
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Alexander A. Sherstov

A strong direct product theorem (SDPT) states that solving $n$ instances of a problem requires $\Omega(n)$ times the resources for a single instance, even to achieve success probability $2^{-\Omega(n)}.$ We prove that quantum communication complexity obeys an SDPT whenever the communication lower bound for a single instance is proved by ... more >>>

Alexander A. Sherstov

We study the set disjointness problem in the number-on-the-forehead model.

(i) We prove that $k$-party set disjointness has randomized and nondeterministic

communication complexity $\Omega(n/4^k)^{1/4}$ and Merlin-Arthur complexity $\Omega(n/4^k)^{1/8}.$

These bounds are close to tight. Previous lower bounds (2007-2008) for $k\geq3$ parties

were weaker than $n^{1/(k+1)}/2^{k^2}$ in all ...
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Andrej Bogdanov, Manuel Sabin, Prashant Nalini Vasudevan

A $k$-LIN instance is a system of $m$ equations over $n$ variables of the form $s_{i[1]} + \dots + s_{i[k]} =$ 0 or 1 modulo 2 (each involving $k$ variables). We consider two distributions on instances in which the variables are chosen independently and uniformly but the right-hand sides are ... more >>>