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REPORTS > KEYWORD > PSEUDORANDOM GENERAORS:
Reports tagged with Pseudorandom generaors:
TR18-183 | 5th November 2018
Dean Doron, Pooya Hatami, William Hoza

#### Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas

Revisions: 2

We give an explicit pseudorandom generator (PRG) for constant-depth read-once formulas over the basis $\{\wedge, \vee, \neg\}$ with unbounded fan-in. The seed length of our PRG is $\widetilde{O}(\log(n/\varepsilon))$. Previously, PRGs with near-optimal seed length were known only for the depth-2 case (Gopalan et al. FOCS '12). For a constant depth ... more >>>

TR19-149 | 4th November 2019
Dean Doron, Pooya Hatami, William Hoza

#### Log-Seed Pseudorandom Generators via Iterated Restrictions

There are only a few known general approaches for constructing explicit pseudorandom generators (PRGs). The iterated restrictions'' approach, pioneered by Ajtai and Wigderson [AW89], has provided PRGs with seed length $\mathrm{polylog} n$ or even $\tilde{O}(\log n)$ for several restricted models of computation. Can this approach ever achieve the optimal seed ... more >>>

TR21-116 | 10th August 2021
Nai-Hui Chia, Chi-Ning Chou, Jiayu Zhang, Ruizhe Zhang

#### Quantum Meets the Minimum Circuit Size Problem

Revisions: 1

In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory---its hardness is mysterious, and a better understanding of its hardness can have ... more >>>

TR22-021 | 19th February 2022
Xin Lyu

#### Improved Pseudorandom Generators for $\mathrm{AC}^0$ Circuits

We give PRG for depth-$d$, size-$m$ $\mathrm{AC}^0$ circuits with seed length $O(\log^{d-1}(m)\log(m/\varepsilon)\log\log(m))$. Our PRG improves on previous work [TX13, ST19, Kel21] from various aspects. It has optimal dependence on $\frac{1}{\varepsilon}$ and is only one “$\log\log(m)$” away from the lower bound barrier. For the case of $d=2$, the seed length tightly ... more >>>

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