Related papers: Counting Subwords and Regular Languages
We study the matching problem of regular tree languages, that is, "$\exists \sigma:\sigma(L)\subseteq R$?" where $L,R$ are regular tree languages over the union of finite ranked alphabets $\Sigma$ and $\mathcal{X}$ where $\mathcal{X}$ is an…
In this paper, we study the pattern occurrence in $k$-ary words. We prove an explicit upper bound on the number of $k$-ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce several already known…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two…
We count the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. More precisely, we consider the sequence $(S_b(n))_{n\ge 0}$ counting the number of positive entries on each row of a…
We prove two results about width of words in $SL_n(\mathbb{Z})$. The first is that, for every $n \geq 3$, there is a constant $C(n)$ such that the width of any word in $SL_n(\mathbb{Z})$ is less than $C(n)$. The second result is that, for…
Regular sound correspondences constitute the principal evidence in historical language comparison. Despite the heuristic focus on regularity, it is often more an intuitive judgement than a quantified evaluation, and irregularity is more…
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested…
We discuss the notion of privileged word, recently introduced by Peltomaki. A word w is privileged if it is of length <=1, or has a privileged border that occurs exactly twice in w. We prove the following results: (1) if w^k is privileged…
This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language \(L\) is REG-measurable if there exists an infinite sequence of regular languages that…
Co-occurrences between two words provide useful insights into the semantics of those words. Consequently, numerous prior work on word embedding learning have used co-occurrences between two words as the training signal for learning word…
A group-word w is called concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is said to be concise in a class of groups X if whenever the set of…
A non-empty word $w$ is a border of the word $u$ if $\vert w\vert<\vert u\vert$ and $w$ is both a prefix and a suffix of $u$. A word $u$ with the border $w$ is closed if $u$ has exactly two occurrences of $w$. A word $u$ is privileged if…
Much of the power of probabilistic methods in modelling language comes from their ability to compare several derivations for the same string in the language. An important starting point for the study of such cross-derivational properties is…
Prefix normal words are binary words in which each prefix has at least the same number of $\so$s as any factor of the same length. Firstly introduced by Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix…
Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to…
In this paper, we describe an approach to sentence categorization which has the originality to be based on natural properties of languages with no training set dependency. The implementation is fast, small, robust and textual errors…
A word over an ordered alphabet is said to be clustering if identical letters appear adjacently in its Burrows-Wheeler transform. Such words are strictly related to (discrete) interval exchange transformations. We use an extended version of…