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Electronic Colloquium on Computational Complexity

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Reports tagged with inner product:
TR12-047 | 24th April 2012
Emanuele Viola

Extractors for Turing-machine sources

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 ... more >>>

TR13-081 | 6th June 2013
Divesh Aggarwal, Yevgeniy Dodis, Shachar Lovett

Non-malleable Codes from Additive Combinatorics

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 >>>

TR16-143 | 15th September 2016
Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan

An Almost Cubic Lower Bound for $\Sigma\Pi\Sigma$ Circuits Computing a Polynomial in VP

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 >>>

TR16-181 | 15th November 2016
Avishay Tal

The Bipartite Formula Complexity of Inner-Product is Quadratic

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 >>>

TR17-014 | 23rd January 2017
Arkadev Chattopadhyay, Michal Koucky, Bruno Loff, Sagnik Mukhopadhyay

Composition and Simulation Theorems via Pseudo-random Properties

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 >>>

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