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Let $g$, $h$ be a random pair of generators of $G=Sym(n)$ or $G=Alt(n)$. We show that, with probability tending to $1$ as $n\to \infty$, (a) the diameter of $G$ with respect to $S = \{g,h,g^{-1},h^{-1}\}$ is at most $O(n^2 (\log n)^c)$, and…

Group Theory · Mathematics 2014-03-11 Harald A. Helfgott , Ákos Seress , Andrzej Zuk

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…

Quantum Physics · Physics 2021-09-29 Michael J. Gullans , Stefan Krastanov , David A. Huse , Liang Jiang , Steven T. Flammia

A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = \mathsf{sign}(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class…

Computational Complexity · Computer Science 2021-11-30 Zander Kelley , Raghu Meka

This article presents a new class of Pseudorandom Number Generators. The generators are based on traversing a n-cube where a Balanced Hamiltonian Cycle has been removed. The construction of such generators is automatic for small number of…

Data Structures and Algorithms · Computer Science 2017-06-28 Jean-François Couchot , Pierre-Cyrille Heam , Christophe Guyeux , Qianxue Wang , Jacques M. Bahi

We study the arithmetic complexity of hitting set generators, which are pseudorandom objects used for derandomization of the polynomial identity testing problem. We give new explicit constructions of hitting set generators whose outputs are…

Computational Complexity · Computer Science 2025-08-19 Robert Andrews

We describe a methodology and standard of proof for experimental claims of quantum random number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations,…

Quantum Physics · Physics 2015-01-14 Morgan W. Mitchell , Carlos Abellan , Waldimar Amaya

In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…

Information Theory · Computer Science 2024-07-11 Roni Con , Zeyu Guo , Ray Li , Zihan Zhang

This paper concerns {\em randomized} leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete $n$-node networks that runs in O(1) rounds and (with high probability) uses only…

Data Structures and Algorithms · Computer Science 2013-05-16 Shay Kutten , Gopal Pandurangan , David Peleg , Peter Robinson , Amitabh Trehan

The aim of this paper is to present a new design for a pseudorandom number generator (PRNG) that is cryptographically secure, passes all of the usual statistical tests referenced in the literature and hence generates high quality random…

Cryptography and Security · Computer Science 2025-03-25 Juan Di Mauro , Eduardo Salazar , Hugo D. Scolnik

NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to…

Cryptography and Security · Computer Science 2014-01-15 Yongge Wang

We devise a new pseudorandom generator against degree 2 polynomial threshold functions in the Gaussian setting. We manage to achieve $\epsilon$ error with seed length polylogarithmic in $\epsilon$ and the dimension, and exponential…

Computational Complexity · Computer Science 2014-04-07 Daniel M. Kane

We present a polynomial-time algorithm for online differentially private synthetic data generation. For a data stream within the hypercube $[0,1]^d$ and an infinite time horizon, we develop an online algorithm that generates a…

Statistics Theory · Mathematics 2024-10-31 Yiyun He , Roman Vershynin , Yizhe Zhu

A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are…

Cryptography and Security · Computer Science 2020-11-20 Luca Pasqualini , Maurizio Parton

Sub-categories of mathematical topology, like the mathematical theory of chaos, offer interesting applications devoted to information security. In this research work, we have introduced a new chaos-based pseudorandom number generator…

Cryptography and Security · Computer Science 2017-06-27 Mohammed Bakiri , Jean-François Couchot , Christophe Guyeux

We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive,…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-27 Mohammad T. Hajiaghayi , Dariusz R. Kowalski , Jan Olkowski

Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…

Numerical Analysis · Mathematics 2025-02-26 El-Mehdi El Arar , Massimiliano Fasi , Silviu-Ioan Filip , Mantas Mikaitis

Pseudo-Random Numbers Generators (PRNGs) are algorithms produced to generate long sequences of statistically uncorrelated numbers, i.e. Pseudo-Random Numbers (PRNs). These numbers are widely employed in mid-level cryptography and in…

Cryptography and Security · Computer Science 2019-12-30 Luca Pasqualini , Maurizio Parton

We develop the theory of cryptographic nondeterministic-secure pseudorandomness beyond the point reached by Rudich's original work (Rudich 1997), and apply it to draw new consequences in average-case complexity and proof complexity.…

Computational Complexity · Computer Science 2025-01-14 Iddo Tzameret , Lu-Ming Zhang

A central approach to algorithmic derandomization is to construct probability distributions with small support that "fool" randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling…

Data Structures and Algorithms · Computer Science 2026-01-27 Jeff Giliberti , David G. Harris

A select collection of pseudorandom number generators is applied to a Monte Carlo study of the two dimensional square site percolation model. A generator suitable for high precision calculations is identified from an application specific…

Disordered Systems and Neural Networks · Physics 2009-11-13 Michael J. Lee