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REPORTS > AUTHORS > ROEI TELL:
All reports by Author Roei Tell:

TR18-199 | 24th November 2018
Lijie Chen, Roei Tell

Bootstrapping Results for Threshold Circuits “Just Beyond” Known Lower Bounds

The best-known lower bounds for the circuit class $\mathcal{TC}^0$ are only slightly super-linear. Similarly, the best-known algorithm for derandomization of this class is an algorithm for quantified derandomization (i.e., a weak type of derandomization) of circuits of slightly super-linear size. In this paper we show that even very mild quantitative ... more >>>


TR18-159 | 11th September 2018
Igor Carboni Oliveira, Rahul Santhanam, Roei Tell

Expander-Based Cryptography Meets Natural Proofs

Revisions: 1

We introduce new forms of attack on expander-based cryptography, and in particular on Goldreich's pseudorandom generator and one-way function. Our attacks exploit low circuit complexity of the underlying expander's neighbor function and/or of the local predicate. Our two key conceptual contributions are:

* The security of Goldreich's PRG and OWF ... more >>>


TR18-003 | 2nd January 2018
Roei Tell

Proving that prBPP=prP is as hard as "almost" proving that P \ne NP

Revisions: 2

We show that any proof that $promise\textrm{-}\mathcal{BPP}=promise\textrm{-}\mathcal{P}$ necessitates proving circuit lower bounds that almost yield that $\mathcal{P}\ne\mathcal{NP}$. More accurately, we show that if $promise\textrm{-}\mathcal{BPP}=promise\textrm{-}\mathcal{P}$, then for essentially any super-constant function $f(n)=\omega(1)$ it holds that $NTIME[n^{f(n)}]\not\subseteq\mathcal{P}/\mathrm{poly}$. The conclusion of the foregoing conditional statement cannot be improved (to conclude that $\mathcal{NP}\not\subseteq\mathcal{P}/\mathrm{poly}$) without ... more >>>


TR17-187 | 3rd December 2017
Roei Tell

A Note on the Limitations of Two Black-Box Techniques in Quantified Derandomization

The quantified derandomization problem of a circuit class $\mathcal{C}$ with a function $B:\mathbb{N}\rightarrow\mathbb{N}$ is the following: Given an input circuit $C\in\mathcal{C}$ over $n$ bits, deterministically distinguish between the case that $C$ accepts all but $B(n)$ of its inputs and the case that $C$ rejects all but $B(n)$ of its inputs. ... more >>>


TR17-145 | 19th September 2017
Roei Tell

Quantified derandomization of linear threshold circuits

Revisions: 2

One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing approach to prove such lower bounds is to construct a non-trivial derandomization algorithm for ... more >>>


TR16-191 | 24th November 2016
Roei Tell

Improved Bounds for Quantified Derandomization of Constant-Depth Circuits and Polynomials

Revisions: 2

Goldreich and Wigderson (STOC 2014) initiated a study of quantified derandomization, which is a relaxed derandomization problem: For a circuit class $\mathcal{C}$ and a parameter $B=B(n)$, the problem is to decide whether a circuit $C\in\mathcal{C}$ rejects all of its inputs, or accepts all but $B(n)$ of its inputs.

In ... more >>>


TR16-050 | 31st March 2016
Roei Tell

Lower Bounds on Black-Box Reductions of Hitting to Density Estimation

Revisions: 1

We consider the following problem. A deterministic algorithm tries to find a string in an unknown set $S\subseteq\{0,1\}^n$ that is guaranteed to have large density (e.g., $|S|\ge2^{n-1}$). However, the only information that the algorithm can obtain about $S$ is estimates of the density of $S$ in adaptively chosen subsets of ... more >>>


TR16-032 | 10th March 2016
Roei Tell

A Note on Tolerant Testing with One-Sided Error

A tolerant tester with one-sided error for a property is a tester that accepts every input that is close to the property, with probability 1, and rejects every input that is far from the property, with positive probability. In this note we show that such testers require a linear number ... more >>>


TR15-072 | 23rd April 2015
Roei Tell

On Being Far from Far and on Dual Problems in Property Testing

Revisions: 4

For a set $\Pi$ in a metric space and $\delta>0$, denote by $\mathcal{F}_\delta(\Pi)$ the set of elements that are $\delta$-far from $\Pi$. In property testing, a $\delta$-tester for $\Pi$ is required to accept inputs from $\Pi$ and reject inputs from $\mathcal{F}_\delta(\Pi)$. A natural dual problem is the problem of $\delta$-testing ... more >>>


TR14-115 | 27th August 2014
Roei Tell

Deconstructions of Reductions from Communication Complexity to Property Testing using Generalized Parity Decision Trees

Revisions: 1

A few years ago, Blais, Brody, and Matulef (2012) presented a methodology for proving lower bounds for property testing problems by reducing them from problems in communication complexity. Recently, Bhrushundi, Chakraborty, and Kulkarni (2014) showed that some reductions of this type can be deconstructed to two separate reductions, from communication ... more >>>


TR14-114 | 27th August 2014
Roei Tell

An Alternative Proof of an $\Omega(k)$ Lower Bound for Testing $k$-linear Boolean Functions

We provide an alternative proof for a known result stating that $\Omega(k)$ queries are needed to test $k$-sparse linear Boolean functions. Similar to the approach of Blais and Kane (2012), we reduce the proof to the analysis of Hamming weights of vectors in affi ne subspaces of the Boolean hypercube. ... more >>>




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