All reports by Author Roei Tell:

__
TR23-036
| 27th March 2023
__

Dean Doron, Roei Tell#### Derandomization with Minimal Memory Footprint

__
TR22-097
| 3rd July 2022
__

Lijie Chen, Ron D. Rothblum, Roei Tell#### Unstructured Hardness to Average-Case Randomness

__
TR22-087
| 8th June 2022
__

Pooya Hatami, William Hoza, Avishay Tal, Roei Tell#### Depth-$d$ Threshold Circuits vs. Depth-$(d + 1)$ AND-OR Trees

Revisions: 1

__
TR22-057
| 25th April 2022
__

Lijie Chen, Roei Tell#### When Arthur has Neither Random Coins nor Time to Spare: Superfast Derandomization of Proof Systems

Revisions: 2

__
TR21-120
| 18th August 2021
__

Roei Tell#### How to Find Water in the Ocean: A Survey on Quantified Derandomization

__
TR21-080
| 10th June 2021
__

Lijie Chen, Roei Tell#### Hardness vs Randomness, Revised: Uniform, Non-Black-Box, and Instance-Wise

__
TR21-002
| 8th January 2021
__

Pooya Hatami, William Hoza, Avishay Tal, Roei Tell#### Fooling Constant-Depth Threshold Circuits

Revisions: 1

__
TR20-148
| 28th September 2020
__

Lijie Chen, Roei Tell#### Simple and fast derandomization from very hard functions: Eliminating randomness at almost no cost

Revisions: 1

__
TR19-169
| 21st November 2019
__

Lijie Chen, Ron Rothblum, Roei Tell, Eylon Yogev#### On Exponential-Time Hypotheses, Derandomization, and Circuit Lower Bounds

Revisions: 2

__
TR19-119
| 9th September 2019
__

Dean Doron, Amnon Ta-Shma, Roei Tell#### On Hitting-Set Generators for Polynomials that Vanish Rarely

Revisions: 1

__
TR18-199
| 24th November 2018
__

Lijie Chen, Roei Tell#### Bootstrapping Results for Threshold Circuits “Just Beyond” Known Lower Bounds

__
TR18-159
| 11th September 2018
__

Igor Carboni Oliveira, Rahul Santhanam, Roei Tell#### Expander-Based Cryptography Meets Natural Proofs

Revisions: 2

__
TR18-003
| 2nd January 2018
__

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

Revisions: 5

__
TR17-187
| 3rd December 2017
__

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

__
TR17-145
| 19th September 2017
__

Roei Tell#### Quantified derandomization of linear threshold circuits

Revisions: 2

__
TR16-191
| 24th November 2016
__

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

Revisions: 3

__
TR16-050
| 31st March 2016
__

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

Revisions: 1

__
TR16-032
| 10th March 2016
__

Roei Tell#### A Note on Tolerant Testing with One-Sided Error

__
TR15-072
| 23rd April 2015
__

Roei Tell#### On Being Far from Far and on Dual Problems in Property Testing

Revisions: 4

__
TR14-115
| 27th August 2014
__

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

Revisions: 1

__
TR14-114
| 27th August 2014
__

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

Dean Doron, Roei Tell

Existing proofs that deduce BPL=L from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization.

We show that $BPSPACE[S] \subseteq DSPACE[c \cdot S]$ for $c \approx ...
more >>>

Lijie Chen, Ron D. Rothblum, Roei Tell

The leading technical approach in uniform hardness-to-randomness in the last two decades faced several well-known barriers that caused results to rely on overly strong hardness assumptions, and yet still yield suboptimal conclusions.

In this work we show uniform hardness-to-randomness results that *simultaneously break through all of the known barriers*. Specifically, ... more >>>

Pooya Hatami, William Hoza, Avishay Tal, Roei Tell

For $n \in \mathbb{N}$ and $d = o(\log \log n)$, we prove that there is a Boolean function $F$ on $n$ bits and a value $\gamma = 2^{-\Theta(d)}$ such that $F$ can be computed by a uniform depth-$(d + 1)$ $\text{AC}^0$ circuit with $O(n)$ wires, but $F$ cannot be computed ... more >>>

Lijie Chen, Roei Tell

What is the actual cost of derandomization? And can we get it for free? These questions were recently raised by Doron et. al (FOCS 2020) and have been attracting considerable interest. In this work we extend the study of these questions to the setting of *derandomizing interactive proofs systems*.

... more >>>Roei Tell

The focus of this survey is the question of *quantified derandomization*, which was introduced by Goldreich and Wigderson (2014): Does derandomization of probabilistic algorithms become easier if we only want to derandomize algorithms that err with extremely small probability? How small does this probability need to be in order for ... more >>>

Lijie Chen, Roei Tell

We propose a new approach to the hardness-to-randomness framework and to the promise-BPP=promise-P conjecture. Classical results rely on non-uniform hardness assumptions to construct derandomization algorithms that work in the worst-case, or rely on uniform hardness assumptions to construct derandomization algorithms that work only in the average-case. In both types of ... more >>>

Pooya Hatami, William Hoza, Avishay Tal, Roei Tell

We present new constructions of pseudorandom generators (PRGs) for two of the most widely-studied non-uniform circuit classes in complexity theory. Our main result is a construction of the first non-trivial PRG for linear threshold (LTF) circuits of arbitrary constant depth and super-linear size. This PRG fools circuits with depth $d\in\mathbb{N}$ ... more >>>

Lijie Chen, Roei Tell

Extending the classical ``hardness-to-randomness'' line-of-works, Doron et al. (FOCS 2020) recently proved that derandomization with near-quadratic time overhead is possible, under the assumption that there exists a function in $\mathcal{DTIME}[2^n]$ that cannot be computed by randomized SVN circuits of size $2^{(1-\epsilon)\cdot n}$ for a small $\epsilon$.

In this work we ... more >>>

Lijie Chen, Ron Rothblum, Roei Tell, Eylon Yogev

The Exponential-Time Hypothesis ($ETH$) is a strengthening of the $\mathcal{P} \neq \mathcal{NP}$ conjecture, stating that $3\text{-}SAT$ on $n$ variables cannot be solved in time $2^{\epsilon\cdot n}$, for some $\epsilon>0$. In recent years, analogous hypotheses that are ``exponentially-strong'' forms of other classical complexity conjectures (such as $\mathcal{NP}\not\subseteq\mathcal{BPP}$ or $co\text{-}\mathcal{NP}\not\subseteq \mathcal{NP}$) have ... more >>>

Dean Doron, Amnon Ta-Shma, Roei Tell

We study the following question: Is it easier to construct a hitting-set generator for polynomials $p:\mathbb{F}^n\rightarrow\mathbb{F}$ of degree $d$ if we are guaranteed that the polynomial vanishes on at most an $\epsilon>0$ fraction of its inputs? We will specifically be interested in tiny values of $\epsilon\ll d/|\mathbb{F}|$. This question was ... more >>>

Lijie Chen, Roei Tell

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 >>>

Igor Carboni Oliveira, Rahul Santhanam, Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>

Roei Tell

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 >>>