Related papers: Random Formula Generators
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and…
This paper explores the utility of a Large Language Model (LLM) to automatically generate queries and query variants from a description of an information need. Given a set of information needs described as backstories, we explore how…
In Natural Language Generation (NLG) tasks, for any input, multiple communicative goals are plausible, and any goal can be put into words, or produced, in multiple ways. We characterise the extent to which human production varies lexically,…
Random number generators (RNG) are essential elements in many cryptographic systems. True random number generators (TRNG) rely upon sources of randomness from natural processes such as those arising from quantum mechanics phenomena. We…
We note that a rational $3$-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational $3$-tangle diagrams up to isotopy. However, there is no perfect classification about rational…
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…
This paper targets to search so-called \emph{good} generators by doing a brief survey over the generators developed in the history of pseudo-random number generators (PRNGs), verify their claims and rank them based on strong empirical tests…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
In question answering requiring common sense, language models (e.g., GPT-3) have been used to generate text expressing background knowledge that helps improve performance. Yet the cost of working with such models is very high; in this work,…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
Discovery of atomistic systems with desirable properties is a major challenge in chemistry and material science. Here we introduce a novel, autoregressive, convolutional deep neural network architecture that generates molecular equilibrium…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
The goal of the paper is to automatize the selection of mechanisms which are able to describe a set of measurements. In order to do so first we construct a set of possible mechanism fulfilling chemically reasonable requirements with a given…
Conversational AI assistants are becoming popular and question-answering is an important part of any conversational assistant. Using relevant utterances as features in question-answering has shown to improve both the precision and recall…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
The probability that $m$ randomly chosen elements of a finite power associative loop $C$ have prescribed orders and generate $C$ is calculated in terms of certain constants related to the action of $Aut(C)$ on the subloop lattice of $C$. As…