All reports by Author Anna Gal:

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TR19-006
| 17th January 2019
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Anna Gal, Ridwan Syed#### Upper Bounds on Communication in terms of Approximate Rank

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TR18-205
| 3rd December 2018
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Siddhesh Chaubal, Anna Gal#### New Constructions with Quadratic Separation between Sensitivity and Block Sensitivity

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TR18-160
| 12th September 2018
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Anna Gal, Avishay Tal, Adrian Trejo NuĂ±ez#### Cubic Formula Size Lower Bounds Based on Compositions with Majority

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TR14-180
| 22nd December 2014
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Anna Gal, Jing-Tang Jang, Nutan Limaye, Meena Mahajan, Karteek Sreenivasaiah#### Space-Efficient Approximations for Subset Sum

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TR14-127
| 11th October 2014
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Alexandros G. Dimakis, Anna Gal, Ankit Singh Rawat, Zhao Song#### Batch Codes through Dense Graphs without Short Cycles

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TR14-122
| 30th September 2014
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Eric Allender, Anna Gal, Ian Mertz#### Dual VP Classes

Revisions: 2

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TR13-093
| 21st June 2013
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Anna Gal, Jing-Tang Jang#### A Generalization of Spira's Theorem and Circuits with Small Segregators or Separators

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TR12-172
| 8th December 2012
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Mahdi Cheraghchi, Anna Gal, Andrew Mills#### Correctness and Corruption of Locally Decodable Codes

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TR11-150
| 4th November 2011
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Anna Gal, Kristoffer Arnsfelt Hansen, Michal Koucky, Pavel Pudlak, Emanuele Viola#### Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates

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TR11-030
| 9th March 2011
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Anna Gal, Andrew Mills#### Three Query Locally Decodable Codes with Higher Correctness Require Exponential Length

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TR05-136
| 14th November 2005
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Anna Gal, Michal Koucky, Pierre McKenzie#### Incremental branching programs

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TR95-049
| 19th October 1995
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Anna Gal, Avi Wigderson#### Boolean complexity classes vs. their arithmetic analogs

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TR95-001
| 1st January 1995
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Amos Beimel, Anna Gal, Michael S. Paterson#### Lower Bounds for Monotone Span Programs

Anna Gal, Ridwan Syed

We show that any Boolean function with approximate rank $r$ can be computed by bounded error quantum protocols without prior entanglement of complexity $O( \sqrt{r} \log r)$. In addition, we show that any Boolean function with approximate rank $r$ and discrepancy $\delta$ can be computed by deterministic protocols of complexity ... more >>>

Siddhesh Chaubal, Anna Gal

Nisan and Szegedy conjectured that block sensitivity is at most polynomial in sensitivity for any Boolean function. There is a huge gap between the best known upper bound on block sensitivity in terms of sensitivity - which is exponential, and the best known separating examples - which give only a ... more >>>

Anna Gal, Avishay Tal, Adrian Trejo NuĂ±ez

We define new functions based on the Andreev function and prove that they require $n^{3}/polylog(n)$ formula size to compute. The functions we consider are generalizations of the Andreev function using compositions with the majority function. Our arguments apply to composing a hard function with any function that agrees with the ... more >>>

Anna Gal, Jing-Tang Jang, Nutan Limaye, Meena Mahajan, Karteek Sreenivasaiah

SUBSET SUM is a well known NP-complete problem:

given $t \in Z^{+}$ and a set $S$ of $m$ positive integers, output YES if and only if there is a subset $S^\prime \subseteq S$ such that the sum of all numbers in $S^\prime$ equals $t$. The problem and its search ...
more >>>

Alexandros G. Dimakis, Anna Gal, Ankit Singh Rawat, Zhao Song

Consider a large database of $n$ data items that need to be stored using $m$ servers.

We study how to encode information so that a large number $k$ of read requests can be performed \textit{in parallel} while the rate remains constant (and ideally approaches one).

This problem is equivalent ...
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Eric Allender, Anna Gal, Ian Mertz

We consider arithmetic complexity classes that are in some sense dual to the classes VP(Fp) that were introduced by Valiant. This provides new characterizations of the complexity classes ACC^1 and TC^1, and also provides a compelling example of

a class of high-degree polynomials that can be simulated via arithmetic circuits ...
more >>>

Anna Gal, Jing-Tang Jang

Spira showed that any Boolean formula of size $s$ can be simulated in depth $O(\log s)$. We generalize Spira's theorem and show that any Boolean circuit of size $s$ with segregators of size $f(s)$ can be simulated in depth $O(f(s)\log s)$. If the segregator size is at least $s^{\varepsilon}$ for ... more >>>

Mahdi Cheraghchi, Anna Gal, Andrew Mills

Locally decodable codes (LDCs) are error correcting codes with the extra property that it is sufficient to read just a small number of positions of a possibly corrupted codeword in order to recover any one position of the input. To achieve this, it is necessary to use randomness in the ... more >>>

Anna Gal, Kristoffer Arnsfelt Hansen, Michal Koucky, Pavel Pudlak, Emanuele Viola

We bound the minimum number $w$ of wires needed to compute any (asymptotically good) error-correcting code

$C:\{0,1\}^{\Omega(n)} \to \{0,1\}^n$ with minimum distance $\Omega(n)$,

using unbounded fan-in circuits of depth $d$ with arbitrary gates. Our main results are:

(1) If $d=2$ then $w = \Theta(n ({\log n/ \log \log n})^2)$.

(2) ... more >>>

Anna Gal, Andrew Mills

Locally decodable codes

are error correcting codes with the extra property that, in order

to retrieve the correct value of just one position of the input with

high probability, it is

sufficient to read a small number of

positions of the corresponding,

possibly corrupted ...
more >>>

Anna Gal, Michal Koucky, Pierre McKenzie

In this paper we propose the study of a new model of restricted

branching programs which we call incremental branching programs.

This is in line with the program proposed by Cook in 1974 as an

approach for separating the class of problems solvable in logarithmic

space from problems solvable ...
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Anna Gal, Avi Wigderson

This paper provides logspace and small circuit depth analogs

of the result of Valiant-Vazirani, which is a randomized (or

nonuniform) reduction from NP to its arithmetic analog ParityP.

We show a similar randomized reduction between the

Boolean classes NL and semi-unbounded fan-in Boolean circuits and

their arithmetic counterparts. These ...
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Amos Beimel, Anna Gal, Michael S. Paterson

The model of span programs is a linear algebraic model of

computation. Lower bounds for span programs imply lower bounds for

contact schemes, symmetric branching programs and for formula size.

Monotone span programs correspond also to linear secret-sharing schemes.

We present a new technique for proving lower bounds for ...
more >>>