All reports by Author Amir Yehudayoff:

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TR16-151
| 26th September 2016
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Amir Yehudayoff#### Pointer chasing via triangular discrimination

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TR15-164
| 13th October 2015
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Pavel Hrubes, Amir Yehudayoff#### On isoperimetric profiles and computational complexity

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TR15-040
| 24th March 2015
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Shay Moran, Amir Yehudayoff#### Proper PAC learning is compressing

Revisions: 1

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TR15-025
| 22nd February 2015
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Shay Moran, Amir Shpilka, Avi Wigderson, Amir Yehudayoff#### Teaching and compressing for low VC-dimension

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TR14-135
| 23rd October 2014
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Noga Alon, Shay Moran, Amir Yehudayoff#### Sign rank, VC dimension and spectral gaps

Revisions: 2

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TR14-101
| 8th August 2014
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Balthazar Bauer, Shay Moran, Amir Yehudayoff#### Internal compression of protocols to entropy

Revisions: 1

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TR14-060
| 21st April 2014
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Anup Rao, Amir Yehudayoff#### Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness

Revisions: 1

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TR14-046
| 8th April 2014
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Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff#### Approximate Nonnegative Rank is Equivalent to the Smooth Rectangle Bound

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TR14-022
| 19th February 2014
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Shay Moran, Makrand Sinha, Amir Yehudayoff#### Fooling Pairs in Randomized Communication Complexity

Revisions: 1

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TR14-019
| 14th February 2014
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Parikshit Gopalan, Amir Yehudayoff#### Inequalities and tail bounds for elementary symmetric polynomials

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TR13-106
| 29th July 2013
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Shay Moran, Amir Yehudayoff#### A note on average-case sorting

Revisions: 2

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TR13-079
| 2nd June 2013
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Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff#### Direct Sum Fails for Zero Error Average Communication

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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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TR12-143
| 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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TR12-118
| 18th September 2012
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Avi Wigderson, Amir Yehudayoff#### Population Recovery and Partial Identification

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TR12-061
| 16th May 2012
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Pavel Hrubes, Amir Yehudayoff#### Formulas are exponentially stronger than monotone circuits in non-commutative setting

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TR11-160
| 1st December 2011
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Zeev Dvir, Anup Rao, Avi Wigderson, Amir Yehudayoff#### Restriction Access

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TR11-134
| 9th October 2011
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Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff#### Separating multilinear branching programs and formulas

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TR10-149
| 22nd September 2010
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Boaz Barak, Zeev Dvir, Avi Wigderson, Amir Yehudayoff#### Rank Bounds for Design Matrices with Applications to Combinatorial Geometry and Locally Correctable Codes

Revisions: 1

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TR10-040
| 10th March 2010
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Pavel Hrubes, Avi Wigderson, Amir Yehudayoff#### Relationless completeness and separations

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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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TR10-021
| 21st February 2010
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Pavel Hrubes, Avi Wigderson, Amir Yehudayoff#### Non-commutative circuits and the sum-of-squares problem

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TR09-070
| 1st September 2009
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Andrej Bogdanov, Zeev Dvir, Elad Verbin, Amir Yehudayoff#### Pseudorandomness for Width 2 Branching Programs

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TR08-006
| 18th January 2008
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Ran Raz, Amir Yehudayoff#### Lower Bounds and Separations for Constant Depth Multilinear Circuits

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TR07-121
| 21st November 2007
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Zeev Dvir, Amir Shpilka, Amir Yehudayoff#### Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits

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TR07-085
| 2nd September 2007
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Ran Raz, Amir Yehudayoff#### Multilinear Formulas, Maximal-Partition Discrepancy and Mixed-Sources Extractors

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TR06-060
| 4th May 2006
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Ran Raz, Amir Shpilka, Amir Yehudayoff#### A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits

Amir Yehudayoff

We prove an essentially sharp $\tilde\Omega(n/k)$ lower bound on the $k$-round distributional complexity of the $k$-step pointer chasing problem under the uniform distribution, when Bob speaks first. This is an improvement over Nisan and Wigderson's $\tilde \Omega(n/k^2)$ lower bound. A key part of the proof is using triangular discrimination instead ... more >>>

Pavel Hrubes, Amir Yehudayoff

The isoperimetric profile of a graph is a function that measures, for an integer $k$, the size of the smallest edge boundary over all sets of vertices of size $k$. We observe a connection between isoperimetric profiles and computational complexity. We illustrate this connection by an example from communication complexity, ... more >>>

Shay Moran, Amir Yehudayoff

We prove that proper PAC learnability implies compression. Namely, if a concept $C \subseteq \Sigma^X$ is properly PAC learnable with $d$ samples, then $C$ has a sample compression scheme of size $2^{O(d)}$.

In particular, every boolean concept class with constant VC dimension has a sample compression scheme of constant size. ...
more >>>

Shay Moran, Amir Shpilka, Avi Wigderson, Amir Yehudayoff

In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. We present relatively efficient constructions of {\em sample compression schemes} and

for classes of low VC-dimension. Let $C$ be a finite boolean concept class of VC-dimension $d$. Set $k ...
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Noga Alon, Shay Moran, Amir Yehudayoff

We study the maximum possible sign rank of $N \times N$ sign matrices with a given VC dimension $d$. For $d=1$, this maximum is $3$. For $d=2$, this maximum is $\tilde{\Theta}(N^{1/2})$. Similar (slightly less accurate) statements hold for $d>2$ as well. We discuss the tightness of our methods, and describe ... more >>>

Balthazar Bauer, Shay Moran, Amir Yehudayoff

We study internal compression of communication protocols

to their internal entropy, which is the entropy of the transcript from the players' perspective.

We first show that errorless compression to the internal entropy

(and hence to the internal information) is impossible.

We then provide two internal compression schemes with error.

One ...
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Anup Rao, Amir Yehudayoff

We show that the deterministic multiparty communication complexity of set disjointness for $k$ parties on a universe of size $n$ is $\Omega(n/4^k)$. We also simplify Sherstov's proof

showing an $\Omega(\sqrt{n}/(k2^k))$ lower bound for the randomized communication complexity of set disjointness.

Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

We consider two known lower bounds on randomized communication complexity: The smooth rectangle bound and the logarithm of the approximate non-negative rank. Our main result is that they are the same up to a multiplicative constant and a small additive term.

The logarithm of the nonnegative rank is known to ...
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Shay Moran, Makrand Sinha, Amir Yehudayoff

Fooling pairs are one of the standard methods for proving lower bounds for deterministic two-player communication complexity. We study fooling pairs in the context of randomized communication complexity.

We show that every fooling pair induces far away distributions on transcripts of private-coin protocols. We then conclude that the private-coin randomized ...
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Parikshit Gopalan, Amir Yehudayoff

This paper studies the elementary symmetric polynomials $S_k(x)$ for $x \in \mathbb{R}^n$. We show that if $|S_k(x)|,|S_{k+1}(x)|$ are small for some $k>0$ then $|S_\ell(x)|$ is also small for all $\ell > k$. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only $t$-wise ... more >>>

Shay Moran, Amir Yehudayoff

This note studies the average-case comparison-complexity of sorting n elements when there is a known distribution on inputs and the goal is to minimize

the expected number of comparisons. We generalize Fredman's algorithm which

is a variant of insertion sort and provide a basically tight upper bound: If \mu is

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Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

We show that in the model of zero error communication complexity, direct sum fails for average communication complexity as well as for external information cost. Our example also refutes a version of a conjecture by Braverman et al. that in the zero error case amortized communication complexity equals external information ... 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

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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 >>>

Avi Wigderson, Amir Yehudayoff

We study several problems in which an {\em unknown} distribution over an {\em unknown} population of vectors needs to be recovered from partial or noisy samples, each of which nearly completely erases or obliterates the original vector. For example, consider a distribution $p$ over a population $V \subseteq \{0,1\}^n$. A ... more >>>

Pavel Hrubes, Amir Yehudayoff

We give an example of a non-commutative monotone polynomial f which can be computed by a polynomial-size non-commutative formula, but every monotone non-commutative circuit computing f must have an exponential size. In the non-commutative setting this gives, a fortiori, an exponential separation between monotone and general formulas, monotone and general ... more >>>

Zeev Dvir, Anup Rao, Avi Wigderson, Amir Yehudayoff

We introduce a notion of non-black-box access to computational devices (such as circuits, formulas, decision trees, and so forth) that we call \emph{restriction access}. Restrictions are partial assignments to input variables. Each restriction simplifies the device, and yields a new device for the restricted function on the unassigned variables. On ... more >>>

Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff

This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be computationally equivalent to two basic tools in linear algebra: iterated matrix multiplication and the determinant. We compare the computational power of ... more >>>

Boaz Barak, Zeev Dvir, Avi Wigderson, Amir Yehudayoff

A $(q,k,t)$-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most $q$ non-zeros, each column has at least $k$ non-zeros and the supports of every two columns intersect in at most t rows. We prove that the rank ... more >>>

Pavel Hrubes, Avi Wigderson, Amir Yehudayoff

This paper extends Valiant's work on $\vp$ and $\vnp$ to the settings in which variables are not multiplicatively commutative and/or associative. Our main result is a theory of completeness for these algebraic worlds.

We define analogs of Valiant's classes $\vp$ and $\vnp$, as well as of the polynomials permanent ...
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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 >>>

Pavel Hrubes, Avi Wigderson, Amir Yehudayoff

We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of \emph{non-commutative} arithmetic circuits and a problem about \emph{commutative} degree four polynomials, the classical sum-of-squares problem: find the smallest $n$ such that ... more >>>

Andrej Bogdanov, Zeev Dvir, Elad Verbin, Amir Yehudayoff

Bogdanov and Viola (FOCS 2007) constructed a pseudorandom

generator that fools degree $k$ polynomials over $\F_2$ for an arbitrary

constant $k$. We show that such generators can also be used to fool branching programs of width 2 and polynomial length that read $k$ bits of inputs at a

time. This ...
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Ran Raz, Amir Yehudayoff

We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth $d$ ... more >>>

Zeev Dvir, Amir Shpilka, Amir Yehudayoff

In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. More formally, if there exists an explicit polynomial f(x_1,...,x_m) that cannot be computed by a depth d arithmetic circuit of small size then there exists ... more >>>

Ran Raz, Amir Yehudayoff

We study multilinear formulas, monotone arithmetic circuits, maximal-partition discrepancy, best-partition communication complexity and extractors constructions. We start by proving lower bounds for an explicit polynomial for the following three subclasses of syntactically multilinear arithmetic formulas over the field C and the set of variables {x1,...,xn}:

1. Noise-resistant. A syntactically multilinear ... more >>>

Ran Raz, Amir Shpilka, Amir Yehudayoff

We construct an explicit polynomial $f(x_1,...,x_n)$, with

coefficients in ${0,1}$, such that the size of any syntactically

multilinear arithmetic circuit computing $f$ is at least

$\Omega( n^{4/3} / log^2(n) )$. The lower bound holds over any field.