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Language models provide a key framework for studying linguistic theories based on prediction, but phonological analysis using large language models (LLMs) is difficult; there are few phonological benchmarks beyond English and the standard…
We investigate deterministic and randomized streaming algorithms for word problems in finitely generated groups and semigroups. For this we introduce the notion of a distinguisher: a randomized streaming algorithm that processes two input…
As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations ap-pear in research papers, books, lecture notes, blog posts,…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
The inverse relationship between the length of a word and the frequency of its use, first identified by G.K. Zipf in 1935, is a classic empirical law that holds across a wide range of human languages. We demonstrate that length is one…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
There is a wide variety of message-passing communication models, ranging from synchronous ''rendez-vous'' communications to fully asynchronous/out-of-order communications. For large-scale distributed systems, the communication model is…
In this work we extend previous analyses of linguistic networks by adopting a multi-layer network framework for modelling the human mental lexicon, i.e. an abstract mental repository where words and concepts are stored together with their…
When reading a text, it is common to become stuck on unfamiliar words and phrases, such as polysemous words with novel senses, rarely used idioms, internet slang, or emerging entities. If we humans cannot figure out the meaning of those…
A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.
The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…
The rapid growth of the internet has increased the number of online texts. This led to the rapid growth of the number of online texts in the Arabic language. The enormous amount of text must be organized into classes to make the analysis…
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent"…
Recent advances in large language models enable documents to be represented as dense semantic embeddings, supporting similarity-based operations over large text collections. However, many web-scale systems still rely on flat clustering or…
In most cases, word embeddings are learned only from raw tokens or in some cases, lemmas. This includes pre-trained language models like BERT. To investigate on the potential of capturing deeper relations between lexical items and…
We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…
Research in linguistics has shown that humans can read words with internally scrambled letters, a phenomenon recently dubbed typoglycemia. Some specific NLP models have recently been proposed that similarly demonstrate robustness to such…