相关论文: Parikh Motivated Study on Repetitions in Words

We study the regularity of the roots of complex monic polynomials $P(t)$ of fixed degree depending smoothly on a real parameter $t$. We prove that each continuous parameterization of the roots of a generic $C^\infty$ curve $P(t)$ (which…

In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A $d$-dimensional word is called \emph{uniformly recurrent} if for all $(s_1,\ldots,s_d)\in\mathbb{N}^d$ there exists $n\in\mathbb{N}$ such…

We study a conjecture linking ultimate periodicity of infnite words to the existence of colorings on finite words avoiding monochromatic factorisation of suffixes, with the extra condition that the ordered concatenation of elements of this…

We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…

We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be…

After reconsidering the theorem of continuity of the roots of a polynomial in terms of its coefficients in the deformation framework, we study the stability of the greater common divisor of two polynomials compared to perturbations on their…

A \emph{morphism} is a mapping that transforms words through letter-wise substitution, where each symbol is consistently replaced by a fixed word. In the field of combinatorics on words, one topic that has attracted considerable attention…

Pre-trained word embeddings are widely used for transfer learning in natural language processing. The embeddings are continuous and distributed representations of the words that preserve their similarities in compact Euclidean spaces.…

This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…

Fici and Saarela ([2]) conjectured that a binary word of length n contains at least $\lfloor n/4 \rfloor$ abelian squares. We slightly extend this conjecture and show that it holds in some special cases. In all other cases we have the…

Let $u \shuffle v$ denote the set of all shuffles of the words $u$ and $v$. It is shown that for each integer $n \geq 3$ there exists a square-free ternary word $u$ of length $n$ such that $u\shuffle u$ contains a square-free word. This…

A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…

Lack of repeatability and generalisability are two significant threats to continuing scientific development in Natural Language Processing. Language models and learning methods are so complex that scientific conference papers no longer…

An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be…

This paper describes a universal model for paraphrasing that transforms according to defined criteria. We showed that by using different criteria we could construct different kinds of paraphrasing systems including one for answering…

In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…

Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…

We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…

We present a new approach for solving string equations as extensions of Nielsen transformations. Key to our work are the combination of three techniques: a power operator for strings; generalisations of Parikh images; and equality…

An interesting phenomenon in combinatorics on words is when every recurrent word satisfying some avoidance constraints has the same factor set as a morphic word. An early example is the Hall-Thue word, fixed point of the morphism…