Related papers: Aperiodic pseudorandom number generators based on …
The two components for infinite exchangeability of a sequence of distributions $(P_n)$ are (i) consistency, and (ii) finite exchangeability for each $n$. A consequence of the Aldous-Hoover theorem is that any node-exchangeable,…
We prove new results on the polarizing random walk framework introduced in recent works of Chattopadhyay {et al.} [CHHL19,CHLT19] that exploit $L_1$ Fourier tail bounds for classes of Boolean functions to construct pseudorandom generators…
A binary word is Sturmian if the occurrences of each letter are balanced, in the sense that in any two factors of the same length, the difference between the number of occurrences of the same letter is at most 1. In digital geometry,…
Neural Network Language Models (NNLMs) generate probability distributions by applying a softmax function to a distance metric formed by taking the dot product of a prediction vector with all word vectors in a high-dimensional embedding…
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
Let $\{a_\rr : \rr \in (\Z^+)^d \}$ be a $d$-dimensional array of numbers, for which the generating function $F(\zz) := \sum_\rr a_\rr \zz^\rr$ is meromorphic in a neighborhood of the origin. For example, $F$ may be a rational multivariate…
These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor complexity for infinite words. We investigate the following…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
Paper withdrawn; will be replaced by revised version containing application to lattice models as well. We study hierarchical properties of Sturmian words. These properties are similar to those of substitution dynamical systems. This…
We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on k-tuples of words (for every natural number k) over a finite alphabet, can be extended to one for partitions on…
In recent years, numerous incidents involving the leakage of website accounts and text passwords (referred to as passwords) have raised significant concerns regarding the potential exposure of personal information. These events underscore…
Let $W^{(n)}$ be the $n$-letter word obtained by repeating a fixed word $W$, and let $R_n$ be a random $n$-letter word over the same alphabet. We show several results about the length of the longest common subsequence (LCS) between…
This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional…
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n) +2 - P_U(n+1) -…
A right [left] locally testable language S is a language with the property that for some non negative integer k two words u and v in alphabet S are equal in the semi group if (1) the prefix and suffix of the words of length k coincide, (2)…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
Prompt-based methods have been used extensively across NLP to build zero- and few-shot label predictors. Many NLP tasks are naturally structured: that is, their outputs consist of multiple labels which constrain each other. Annotating data…