Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

All reports by Author Amir Yehudayoff:

TR16-151 | 26th September 2016
Amir Yehudayoff

Pointer chasing via triangular discrimination

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 >>>

TR15-164 | 13th October 2015
Pavel Hrubes, Amir Yehudayoff

On isoperimetric profiles and computational complexity

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 >>>

TR15-040 | 24th March 2015
Shay Moran, Amir Yehudayoff

Proper PAC learning is compressing

Revisions: 1

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 >>>

TR15-025 | 22nd February 2015
Shay Moran, Amir Shpilka, Avi Wigderson, Amir Yehudayoff

Teaching and compressing for low VC-dimension

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 ... more >>>

TR14-135 | 23rd October 2014
Noga Alon, Shay Moran, Amir Yehudayoff

Sign rank, VC dimension and spectral gaps

Revisions: 2

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 >>>

TR14-101 | 8th August 2014
Balthazar Bauer, Shay Moran, Amir Yehudayoff

Internal compression of protocols to entropy

Revisions: 1

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 ... more >>>

TR14-060 | 21st April 2014
Anup Rao, Amir Yehudayoff

Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness

Revisions: 1

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.

more >>>

TR14-046 | 8th April 2014
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Approximate Nonnegative Rank is Equivalent to the Smooth Rectangle Bound

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 ... more >>>

TR14-022 | 19th February 2014
Shay Moran, Makrand Sinha, Amir Yehudayoff

Fooling Pairs in Randomized Communication Complexity

Revisions: 1

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 ... more >>>

TR14-019 | 14th February 2014
Parikshit Gopalan, Amir Yehudayoff

Inequalities and tail bounds for elementary symmetric polynomials

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 >>>

TR13-106 | 29th July 2013
Shay Moran, Amir Yehudayoff

A note on average-case sorting

Revisions: 2

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
more >>>

TR13-079 | 2nd June 2013
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Direct Sum Fails for Zero Error Average Communication

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 >>>

TR13-035 | 6th March 2013
Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

Direct product via round-preserving compression

Revisions: 1

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 >>>

TR12-143 | 5th November 2012
Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

Direct Products in Communication Complexity

Revisions: 2

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 >>>

TR12-118 | 18th September 2012
Avi Wigderson, Amir Yehudayoff

Population Recovery and Partial Identification

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 >>>

TR12-061 | 16th May 2012
Pavel Hrubes, Amir Yehudayoff

Formulas are exponentially stronger than monotone circuits in non-commutative setting

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 >>>

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

Restriction Access

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 >>>

TR11-134 | 9th October 2011
Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff

Separating multilinear branching programs and formulas

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 >>>

TR10-149 | 22nd September 2010
Boaz Barak, Zeev Dvir, Avi Wigderson, Amir Yehudayoff

Rank Bounds for Design Matrices with Applications to Combinatorial Geometry and Locally Correctable Codes

Revisions: 1

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 >>>

TR10-040 | 10th March 2010
Pavel Hrubes, Avi Wigderson, Amir Yehudayoff

Relationless completeness and separations

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 ... more >>>

TR10-035 | 7th March 2010
Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff

Pseudorandom Generators for Regular Branching Programs

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 >>>

TR10-021 | 21st February 2010
Pavel Hrubes, Avi Wigderson, Amir Yehudayoff

Non-commutative circuits and the sum-of-squares problem

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 >>>

TR09-070 | 1st September 2009
Andrej Bogdanov, Zeev Dvir, Elad Verbin, Amir Yehudayoff

Pseudorandomness for Width 2 Branching Programs

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 ... more >>>

TR08-006 | 18th January 2008
Ran Raz, Amir Yehudayoff

Lower Bounds and Separations for Constant Depth Multilinear Circuits

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 >>>

TR07-121 | 21st November 2007
Zeev Dvir, Amir Shpilka, Amir Yehudayoff

Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits

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 >>>

TR07-085 | 2nd September 2007
Ran Raz, Amir Yehudayoff

Multilinear Formulas, Maximal-Partition Discrepancy and Mixed-Sources Extractors

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 >>>

TR06-060 | 4th May 2006
Ran Raz, Amir Shpilka, Amir Yehudayoff

A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits

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.

more >>>

ISSN 1433-8092 | Imprint