All reports by Author Mark Braverman:

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TR22-179
| 16th December 2022
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Mark Braverman, Klim Efremenko, Gillat Kol, Raghuvansh Saxena, Zhijun Zhang#### Round-vs-Resilience Tradeoffs for Binary Feedback Channels

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TR22-167
| 23rd November 2022
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Mark Braverman, Subhash Khot, Dor Minzer#### Parallel Repetition for the GHZ Game: Exponential Decay

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TR21-083
| 21st June 2021
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Mark Braverman, Sumegha Garg, Or Zamir#### Tight Space Complexity of the Coin Problem

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TR20-139
| 11th September 2020
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Mark Braverman, Sumegha Garg, David Woodruff#### The Coin Problem with Applications to Data Streams

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TR19-141
| 22nd October 2019
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Mark Braverman, Subhash Khot, Dor Minzer#### On Rich $2$-to-$1$ Games

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TR17-182
| 21st November 2017
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Mark Braverman, Young Kun Ko#### Information Value of Two-Prover Games

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TR17-161
| 30th October 2017
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Mark Braverman, Gil Cohen, Sumegha Garg#### Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

Revisions: 1

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TR16-166
| 1st November 2016
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Mark Braverman, Ran Gelles, Michael A. Yitayew#### Optimal Resilience for Short-Circuit Noise in Formulas

Revisions: 1

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TR15-197
| 7th December 2015
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Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler#### Constant-rate coding for multiparty interactive communication is impossible

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TR15-081
| 12th May 2015
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Mark Braverman, Ankit Garg, Young Kun Ko, Jieming Mao, Dave Touchette#### Near-optimal bounds on bounded-round quantum communication complexity of disjointness

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TR15-074
| 29th April 2015
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Mark Braverman, Young Kun Ko, Aviad Rubinstein, Omri Weinstein#### ETH Hardness for Densest-$k$-Subgraph with Perfect Completeness

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TR15-023
| 10th February 2015
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Mark Braverman, Jon Schneider#### Information complexity is computable

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TR15-014
| 18th January 2015
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Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler#### Reliable Communication over Highly Connected Noisy Networks

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TR15-002
| 2nd January 2015
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Mark Braverman, Rotem Oshman#### The Communication Complexity of Number-In-Hand Set Disjointness with No Promise

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TR14-119
| 15th September 2014
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Mark Braverman, Jieming Mao#### Simulating Noisy Channel Interaction

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TR14-095
| 24th July 2014
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Mark Braverman, Ankit Garg#### Small value parallel repetition for general games

Revisions: 1

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TR14-092
| 22nd July 2014
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Mark Braverman, Young Kun Ko, Omri Weinstein#### Approximating the best Nash Equilibrium in $n^{o(\log n)}$-time breaks the Exponential Time Hypothesis

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TR14-047
| 8th April 2014
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Mark Braverman, Omri Weinstein#### An Interactive Information Odometer with Applications

Revisions: 1

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TR14-013
| 30th January 2014
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Mark Braverman, Kanika Pasricha#### The computational hardness of pricing compound options

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TR14-007
| 17th January 2014
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Mark Braverman, Klim Efremenko#### List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise

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TR13-130
| 17th September 2013
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Mark Braverman, Ankit Garg#### Public vs private coin in bounded-round information

Revisions: 1

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TR13-035
| 6th March 2013
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Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff#### Direct product via round-preserving compression

Revisions: 1

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TR12-177
| 19th December 2012
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Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein#### Information lower bounds via self-reducibility

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TR12-171
| 3rd December 2012
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Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein#### From Information to Exact Communication

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TR12-143
| 5th November 2012
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Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff#### Direct Products in Communication Complexity

Revisions: 2

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TR12-131
| 18th October 2012
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Mark Braverman, Ankur Moitra#### An Information Complexity Approach to Extended Formulations

Revisions: 1

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TR11-164
| 9th December 2011
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Mark Braverman, Omri Weinstein#### A discrepancy lower bound for information complexity

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TR11-123
| 15th September 2011
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Mark Braverman#### Interactive information complexity

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TR11-064
| 23rd April 2011
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Mark Braverman#### Towards deterministic tree code constructions

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TR10-166
| 5th November 2010
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Mark Braverman, Anup Rao#### Towards Coding for Maximum Errors in Interactive Communication

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TR10-083
| 13th May 2010
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Mark Braverman, Anup Rao#### Efficient Communication Using Partial Information

Revisions: 1

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TR10-035
| 7th March 2010
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Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff#### Pseudorandom Generators for Regular Branching Programs

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TR09-044
| 6th May 2009
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Boaz Barak, Mark Braverman, Xi Chen, Anup Rao#### Direct Sums in Randomized Communication Complexity

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TR09-011
| 31st January 2009
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Mark Braverman#### Poly-logarithmic independence fools AC0 circuits

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TR07-035
| 3rd April 2007
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Mark Braverman, Raghav Kulkarni, Sambuddha Roy#### Parity Problems in Planar Graphs

Mark Braverman, Klim Efremenko, Gillat Kol, Raghuvansh Saxena, Zhijun Zhang

In a celebrated result from the $60$'s, Berlekamp showed that feedback can be used to increase the maximum fraction of adversarial noise that can be tolerated by binary error correcting codes from $1/4$ to $1/3$. However, his result relies on the assumption that feedback is "continuous", i.e., after every utilization ... more >>>

Mark Braverman, Subhash Khot, Dor Minzer

We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.

more >>>Mark Braverman, Sumegha Garg, Or Zamir

In the coin problem we are asked to distinguish, with probability at least $2/3$, between $n$ $i.i.d.$ coins which are heads with probability $\frac{1}{2}+\beta$ from ones which are heads with probability $\frac{1}{2}-\beta$. We are interested in the space complexity of the coin problem, corresponding to the width of a read-once ... more >>>

Mark Braverman, Sumegha Garg, David Woodruff

Consider the problem of computing the majority of a stream of $n$ i.i.d. uniformly random bits. This problem, known as the {\it coin problem}, is central to a number of counting problems in different data stream models. We show that any streaming algorithm for solving this problem with large constant ... more >>>

Mark Braverman, Subhash Khot, Dor Minzer

We propose a variant of the $2$-to-$1$ Games Conjecture that we call the Rich $2$-to-$1$ Games Conjecture and show that it is equivalent to the Unique Games Conjecture. We are motivated by two considerations. Firstly, in light of the recent proof of the $2$-to-$1$ Games Conjecture, we hope to understand ... more >>>

Mark Braverman, Young Kun Ko

We introduce a generalization of the standard framework for studying the difficulty of two-prover games. Specifically, we study the model where Alice and Bob are allowed to communicate (with information constraints) --- in contrast to the usual two-prover game where they are not allowed to communicate after receiving their respective ... more >>>

Mark Braverman, Gil Cohen, Sumegha Garg

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>

Mark Braverman, Ran Gelles, Michael A. Yitayew

We show an efficient method for converting a logic circuit of gates with fan-out 1 into an equivalent circuit that works even if some fraction of its gates are short-circuited, i.e., their output is short-circuited to one of their inputs. Our conversion can be applied to any circuit with fan-in ... more >>>

Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability $\epsilon$. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise.

Our ... more >>>

Mark Braverman, Ankit Garg, Young Kun Ko, Jieming Mao, Dave Touchette

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r)$ on the communication required for computing disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound ... more >>>

Mark Braverman, Young Kun Ko, Aviad Rubinstein, Omri Weinstein

We show that, assuming the (deterministic) Exponential Time Hypothesis, distinguishing between a graph with an induced $k$-clique and a graph in which all $k$-subgraphs have density at most $1-\epsilon$, requires $n^{\tilde \Omega(log n)}$ time. Our result essentially matches the quasi-polynomial algorithms of Feige and Seltser [FS97] and Barman [Bar15] for ... more >>>

Mark Braverman, Jon Schneider

The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function $f$ to within any additive error $\alpha>0$, thus resolving an ... more >>>

Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

We consider the task of multiparty computation performed over networks in

the presence of random noise. Given an $n$-party protocol that takes $R$

rounds assuming noiseless communication, the goal is to find a coding

scheme that takes $R'$ rounds and computes the same function with high

probability even when the ...
more >>>

Mark Braverman, Rotem Oshman

Set disjointness is one of the most fundamental problems in communication complexity. In the multi-party number-in-hand version of set disjointness, $k$ players receive private inputs $X_1,\ldots,X_k\subseteq \{1,\ldots,n\}$, and their goal is to determine whether or not $\bigcap_{i = 1}^k X_i = \emptyset$. In this paper we prove a tight lower ... more >>>

Mark Braverman, Jieming Mao

We show that $T$ rounds of interaction over the binary symmetric channel $BSC_{1/2-\epsilon}$ with feedback can be simulated with $O(\epsilon^2 T)$ rounds of interaction over a noiseless channel. We also introduce a more general "energy cost'' model of interaction over a noisy channel. We show energy cost to be equivalent ... more >>>

Mark Braverman, Ankit Garg

We prove a parallel repetition theorem for general games with value tending to 0. Previously Dinur and Steurer proved such a theorem for the special case of projection games. We use information theoretic techniques in our proof. Our proofs also extend to the high value regime (value close to 1) ... more >>>

Mark Braverman, Young Kun Ko, Omri Weinstein

The celebrated PPAD hardness result for finding an exact Nash equilibrium in a two-player game

initiated a quest for finding \emph{approximate} Nash equilibria efficiently, and is one of the major open questions in algorithmic game theory.

We study the computational complexity of finding an $\eps$-approximate Nash equilibrium with good social ... more >>>

Mark Braverman, Omri Weinstein

We introduce a novel technique which enables two players to maintain an estimate of the internal information cost of their conversation in an online fashion without revealing much extra information. We use this construction to obtain new results about communication complexity and information-theoretically secure computation.

As a first corollary, ... more >>>

Mark Braverman, Kanika Pasricha

It is generally assumed that you can make a financial asset out of any underlying event or combination thereof, and then sell a security. We show that while this is theoretically true from the financial engineering perspective, compound securities might be intractable to price. Even given no information asymmetries, or ... more >>>

Mark Braverman, Klim Efremenko

In this paper we extend the notion of list decoding to the setting of interactive communication and study its limits. In particular, we show that any protocol can be encoded, with a constant rate, into a list-decodable protocol which is resilient

to a noise rate of up to $1/2-\varepsilon$, ...
more >>>

Mark Braverman, Ankit Garg

We precisely characterize the role of private randomness in the ability of Alice to send a message to Bob while minimizing the amount of information revealed to him. We show that if using private randomness a message can be transmitted while revealing $I$ bits of information, the transmission can be ... more >>>

Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

We obtain a strong direct product theorem for two-party bounded round communication complexity.

Let suc_r(\mu,f,C) denote the maximum success probability of an r-round communication protocol that uses

at most C bits of communication in computing f(x,y) when (x,y)~\mu.

Jain et al. [JPY12] have recently showed that if

more >>>

Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform ... more >>>

Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

We develop a new local characterization of the zero-error information complexity function for two party communication problems, and use it to compute the exact internal and external information complexity of the 2-bit AND function: $IC(AND,0) = C_{\wedge}\approx 1.4923$ bits, and $IC^{ext}(AND,0) = \log_2 3 \approx 1.5839$ bits. This leads to ... more >>>

Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

We give exponentially small upper bounds on the success probability for computing the direct product of any function over any distribution using a communication protocol. Let suc(?,f,C) denote the maximum success probability of a 2-party communication protocol for computing f(x,y) with C bits of communication, when the inputs (x,y) are ... more >>>

Mark Braverman, Ankur Moitra

We prove an unconditional lower bound that any linear program that achieves an $O(n^{1-\epsilon})$ approximation for clique has size $2^{\Omega(n^\epsilon)}$. There has been considerable recent interest in proving unconditional lower bounds against any linear program. Fiorini et al proved that there is no polynomial sized linear program for traveling salesman. ... more >>>

Mark Braverman, Omri Weinstein

This paper provides the first general technique for proving information lower bounds on two-party

unbounded-rounds communication problems. We show that the discrepancy lower bound, which

applies to randomized communication complexity, also applies to information complexity. More

precisely, if the discrepancy of a two-party function $f$ with respect ...
more >>>

Mark Braverman

The primary goal of this paper is to define and study the interactive information complexity of functions. Let $f(x,y)$ be a function, and suppose Alice is given $x$ and Bob is given $y$. Informally, the interactive information complexity $IC(f)$ of $f$ is the least amount of information Alice and Bob ... more >>>

Mark Braverman

We present a deterministic operator on tree codes -- we call tree code product -- that allows one to deterministically combine two tree codes into a larger tree code. Moreover, if the original tree codes are efficiently encodable and decodable, then so is their product. This allows us to give ... more >>>

Mark Braverman, Anup Rao

We show that it is possible to encode any communication protocol

between two parties so that the protocol succeeds even if a $(1/4 -

\epsilon)$ fraction of all symbols transmitted by the parties are

corrupted adversarially, at a cost of increasing the communication in

the protocol by a constant factor ...
more >>>

Mark Braverman, Anup Rao

We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver.

We ... more >>>

Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff

We give new pseudorandom generators for \emph{regular} read-once branching programs of small width.

A branching program is regular if the in-degree of every vertex in it is (0 or) $2$.

For every width $d$ and length $n$,

our pseudorandom generator uses a seed of length $O((\log d + \log\log n ...
more >>>

Boaz Barak, Mark Braverman, Xi Chen, Anup Rao

Does computing n copies of a function require n times the computational effort? In this work, we

give the first non-trivial answer to this question for the model of randomized communication

complexity.

We show that:

1. Computing n copies of a function requires sqrt{n} times the ... more >>>

Mark Braverman

We prove that poly-sized AC0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has ... more >>>

Mark Braverman, Raghav Kulkarni, Sambuddha Roy

We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2^k, for constant k. ... more >>>