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TR18-142 | 17th August 2018
Kaave Hosseini, Shachar Lovett

#### A bilinear Bogolyubov-Ruzsa lemma with poly-logarithmic bounds

The Bogolyubov-Ruzsa lemma, in particular the quantitative bounds obtained by Sanders, plays a central role
in obtaining effective bounds for the inverse $U^3$ theorem for the Gowers norms. Recently, Gowers and Mili\'cevi\'c
applied a bilinear Bogolyubov-Ruzsa lemma as part of a proof of the inverse $U^4$ theorem
with effective bounds.
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TR18-141 | 6th August 2018
Sandip Sinha, Omri Weinstein

#### Local Decodability of the Burrows-Wheeler Transform

The Burrows-Wheeler Transform (BWT) is among the most influential discoveries in text compression and DNA storage. It is a \emph{reversible} preprocessing step that rearranges an $n$-letter string into runs of identical characters (by exploiting context regularities), resulting in highly compressible strings, and is the basis for the ubiquitous \texttt{bzip} program. ... more >>>

TR18-140 | 11th August 2018
Ilan Komargodski, Ran Raz, Yael Tauman Kalai

#### A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols

In 1985, Ben-Or and Linial (Advances in Computing Research '89) introduced the collective coin-flipping problem, where $n$ parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party ... more >>>

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