Emanuele Viola

We obtain the first deterministic randomness extractors

for $n$-bit sources with min-entropy $\ge n^{1-\alpha}$

generated (or sampled) by single-tape Turing machines

running in time $n^{2-16 \alpha}$, for all sufficiently

small $\alpha > 0$. We also show that such machines

cannot sample a uniform $n$-bit input to the Inner

Product function ...
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Divesh Aggarwal, Yevgeniy Dodis, Shachar Lovett

Non-malleable codes provide a useful and meaningful security guarantee in situations where traditional error-correction (and even error-detection) is impossible; for example, when the attacker can completely overwrite the encoded message. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a ... more >>>

Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan

In this note, we prove that there is an explicit polynomial in VP such that any $\Sigma\Pi\Sigma$ arithmetic circuit computing it must have size at least $n^{3-o(1)}$. Up to $n^{o(1)}$ factors, this strengthens a recent result of Kayal, Saha and Tavenas (ICALP 2016) which gives a polynomial in VNP with ... more >>>

Avishay Tal

A bipartite formula on binary variables $x_1, \ldots, x_n$ and $y_1, \ldots, y_n$ is a binary tree whose internal nodes are marked with AND or OR gates and whose leaves may compute any function of either the $x$ or $y$ variables. We show that any bipartite formula for the Inner-Product ... more >>>

Arkadev Chattopadhyay, Michal Koucky, Bruno Loff, Sagnik Mukhopadhyay

We prove a randomized communication-complexity lower bound for a composed OrderedSearch $\circ$ IP — by lifting the randomized query-complexity lower-bound of OrderedSearch to the communication-complexity setting. We do this by extending ideas from a paper of Raz and Wigderson. We think that the techniques we develop will be useful in ... more >>>

Amir Yehudayoff

We prove anti-concentration for the inner product of two independent random vectors in the discrete cube. Our results imply Chakrabarti and Regev's lower bound on the randomized communication complexity of the gap-hamming problem. They are also meaningful in the context of randomness extraction. The proof provides a framework for establishing ... more >>>