相关论文: Testing D-Sequences for their Randomness
We study a modification of Kendall's tau-test, replacing his permutations of n different numbers by sequences of length n, where repetition is allowed. In particular, binary sequences are included. Random sequences can be tested.
This paper investigates the use of quasigroups, Hadamard transforms and Number Theoretic Transforms for use in sequence randomization. This can also be used to generate hash functions for sequence encryption.
We have introduced in former work the concept of Deep Randomness and its interest to design Unconditionally Secure communication protocols. We have in particular given an example of such protocol and introduced how to design a Deep Random…
Certified randomness can be generated with untrusted remote quantum computers using multiple known protocols, one of which has been recently realized experimentally. Unlike the randomness sources accessible on today's classical computers,…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
This paper introduces several depths for random sets with possibly non-convex realisations, proposes ways to estimate the depths based on the samples and compares them with existing ones. The depths are further applied for the comparison…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this probability turns out to be the same for all these notions, so…
This article is meant to provide an additional point of view, applying known knowledge, to supply keys that have a series of non-repeating digits, in a manner that is not usually thought of. Traditionally, prime numbers are used in…
This paper presents a twist to the generation of binary random sequences by starting with decimal sequences. Rather than representing the prime reciprocal sequence directly in base 2, we first right the prime reciprocal in base 10 and then…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
This article is meant to provide an additional point of view, applying known knowledge, to supply keys that have a series of non-repeating digits, in a manner that is not usually thought of. Traditionally, prime numbers are used in…
An approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…