All reports by Author Tom Gur:

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TR18-008
| 10th January 2018
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Tom Gur, Igor Shinkar#### An Entropy Lower Bound for Non-Malleable Extractors

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TR17-155
| 13th October 2017
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Alessandro Chiesa, Tom Gur#### Proofs of Proximity for Distribution Testing

Revisions: 1

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TR17-143
| 26th September 2017
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Tom Gur, Govind Ramnarayan, Ron Rothblum#### Relaxed Locally Correctable Codes

Revisions: 1

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TR17-029
| 18th February 2017
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Clement Canonne, Tom Gur#### An Adaptivity Hierarchy Theorem for Property Testing

Revisions: 1

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TR16-192
| 25th November 2016
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Oded Goldreich, Tom Gur#### Universal Locally Verifiable Codes and 3-Round Interactive Proofs of Proximity for CSP

Revisions: 1
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Comments: 1

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TR16-168
| 2nd November 2016
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Eric Blais, Clement Canonne, Tom Gur#### Alice and Bob Show Distribution Testing Lower Bounds (They don't talk to each other anymore.)

Revisions: 1

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TR16-042
| 19th March 2016
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Oded Goldreich, Tom Gur#### Universal Locally Testable Codes

Revisions: 2

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TR15-024
| 16th February 2015
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Oded Goldreich, Tom Gur, Ron Rothblum#### Proofs of Proximity for Context-Free Languages and Read-Once Branching Programs

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TR14-025
| 25th February 2014
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Oded Goldreich, Tom Gur, Ilan Komargodski#### Strong Locally Testable Codes with Relaxed Local Decoders

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TR13-078
| 28th May 2013
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Tom Gur, Ron Rothblum#### Non-Interactive Proofs of Proximity

Revisions: 1

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TR13-020
| 2nd February 2013
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Tom Gur, Ran Raz#### Arthur-Merlin Streaming Complexity

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TR12-031
| 4th April 2012
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Tom Gur, Omer Tamuz#### Testing Booleanity and the Uncertainty Principle

Revisions: 1

Tom Gur, Igor Shinkar

A (k,\eps)-non-malleable extractor is a function nmExt : {0,1}^n x {0,1}^d -> {0,1} that takes two inputs, a weak source X~{0,1}^n of min-entropy k and an independent uniform seed s in {0,1}^d, and outputs a bit nmExt(X, s) that is \eps-close to uniform, even given the seed s and the ... more >>>

Alessandro Chiesa, Tom Gur

Distribution testing is an area of property testing that studies algorithms that receive few samples from a probability distribution D and decide whether D has a certain property or is far (in total variation distance) from all distributions with that property. Most natural properties of distributions, however, require a large ... more >>>

Tom Gur, Govind Ramnarayan, Ron Rothblum

Locally decodable codes (LDCs) and locally correctable codes (LCCs) are error-correcting codes in which individual bits of the message and codeword, respectively, can be recovered by querying only few bits from a noisy codeword. These codes have found numerous applications both in theory and in practice.

A natural relaxation of ... more >>>

Clement Canonne, Tom Gur

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of \emph{adaptive} testing algorithms, wherein each query may be determined by the answers received to prior queries, and their \emph{non-adaptive} counterparts, in which all ... more >>>

Oded Goldreich, Tom Gur

Universal locally testable codes (Universal-LTCs), recently introduced in our companion paper [GG16], are codes that admit local tests for membership in numerous possible subcodes, allowing for testing properties of the encoded message. In this work, we initiate the study of the NP analogue of these codes, wherein the testing procedures ... more >>>

Eric Blais, Clement Canonne, Tom Gur

We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef [BBM12], we show a simple way to reduce (private-coin) SMP problems to distribution testing problems. This method ... more >>>

Oded Goldreich, Tom Gur

We initiate a study of ``universal locally testable codes" (universal-LTCs). These codes admit local tests for membership in numerous possible subcodes, allowing for testing properties of the encoded message. More precisely, a universal-LTC $C:\{0,1\}^k \to \{0,1\}^n$ for a family of functions $\mathcal{F} = \{ f_i : \{0,1\}^k \to \{0,1\} \}_{i ... more >>>

Oded Goldreich, Tom Gur, Ron Rothblum

Proofs of proximity are probabilistic proof systems in which the verifier only queries a sub-linear number of input bits, and soundness only means that, with high probability, the input is close to an accepting input. In their minimal form, called Merlin-Arthur proofs of proximity (MAP), the verifier receives, in addition ... more >>>

Oded Goldreich, Tom Gur, Ilan Komargodski

Locally testable codes (LTCs) are error-correcting codes

that admit very efficient codeword tests. An LTC is said to

be strong if it has a proximity-oblivious tester;

that is, a tester that makes only a constant number of queries

and reject non-codewords with probability that depends solely

on their distance from ...
more >>>

Tom Gur, Ron Rothblum

We initiate a study of non-interactive proofs of proximity. These proof-systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even read the entire ... more >>>

Tom Gur, Ran Raz

We study the power of Arthur-Merlin probabilistic proof systems in the data stream model. We show a canonical $\mathcal{AM}$ streaming algorithm for a wide class of data stream problems. The algorithm offers a tradeoff between the length of the proof and the space complexity that is needed to verify it.

... more >>>Tom Gur, Omer Tamuz

Let $f:\{-1,1\}^n \to \mathbb{R}$ be a real function on the hypercube, given

by its discrete Fourier expansion, or, equivalently, represented as

a multilinear polynomial. We say that it is Boolean if its image is

in $\{-1,1\}$.

We show that every function on the hypercube with a ... more >>>