Related papers: Effective Generation of Subjectively Random Binary…
Brakerski et. al [BCM+18] introduced the model of cryptographic testing of a single untrusted quantum device and gave a protocol for certifiable randomness generation. We use the leakage resilience properties of the Learning With Errors…
There are many areas of scientific endeavour where large, complex datasets are needed for benchmarking. Evolutionary computing provides a means towards creating such sets. As a case study, we consider Conway's Surreal numbers. They have…
Grammatical inference is a machine learning area, whose fundamentals are built around learning sets. At present, real-life data and examples from manually crafted grammars are used to test their learning performance. This paper aims to…
We present a new approach to constructing of pseudo-random binary sequences (PRS) generators for the purpose of cryptographic data protection, secured from the perpetrator's attacks, caused by generation of masses of hardware errors and…
Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy.…
We consider a rank 1 valuation $\nu$ centered in a regular 3-dimensional local ring $R$. We assume that the residue field $k$ of $\nu$ is contained in $R$. An algorithm for constructing a generating sequences for $\nu$ in $R$ is provided.…
Automatic generation of sequences has been a highly explored field in the last years. In particular, natural language processing and automatic music composition have gained importance due to the recent advances in machine learning and…
We study how to generate binary de Bruijn sequences efficiently from the class of simple linear feedback shift registers with feedback function $f(x_0, x_1, \ldots, x_{n-1}) = x_0 + x_1 + x_{n-1}$ for $n \geq 3$, using the cycle joining…
Let $N(n,r,k)$ denote the number of binary words of length $n$ that begin with $0$ and contain exactly $k$ runs (i.e., maximal subwords of identical consecutive symbols) of length $r$. We show that the generating function for the sequence…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
We develop a very simple compensated scheme for computing very accurate Givens rotations. The approach is significantly more straightforward than the one in \cite{borges2021fast}, and the derivation leads to a very satisfying algorithm…
We revisit the traditional framework of wireless secret key generation, where two parties leverage the wireless channel randomness to establish a secret key. The essence in the framework is to quantify channel randomness into bit sequences…
The Gamma distribution is well-known and widely used in many signal processing and communications applications. In this letter, a simple and extremely efficient accept/reject algorithm is introduced for the generation of independent random…
Motivated by EEG recordings of normal brain activity, we construct arbitrarily large McCulloch-Pitts neural networks that, without any external input, make every subset of their neurons fire in some iteration (and therefore in infinitely…
In this paper we consider a transformer with an $n$-gram structure, such as the one underlying ChatGPT. The transformer provides next word probabilities, which can be used to generate word sequences. We consider methods for computing word…
Story generation is a task that aims to automatically produce multiple sentences to make up a meaningful story. This task is challenging because it requires high-level understanding of semantic meaning of sentences and causality of story…
We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to bias the output bit towards a preferred value. For weak coin…
Adequate sampling space coverage is the keystone to effectively train trustworthy Machine Learning models. Unfortunately, real data do carry several inherent risks due to the many potential biases they exhibit when gathered without a proper…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…