Related papers: Well-Quasi-Orderings on Word Languages

A prefix normal word is a binary word whose prefixes contain at least as many 1s as any of its factors of the same length. Introduced by Fici and Lipt\'ak in 2011 the notion of prefix normality is so far only defined for words over the…

We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…

This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…

A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in the same way, where by subword we mean subsequence. We study the quotient…

Higher-order grammars are extensions of regular and context-free grammars, where non-terminals may take parameters. They have been extensively studied in 1980's, and restudied recently in the context of model checking and program…

We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups.

We study the well-quasi-order (wqo) consisting of the set of finite trees with leaf labels coming from an arbitrary wqo $Q$, ordered by tree homomorphisms which respect the order on the labels. This is a variant of the usual Kruskal tree…

Why do some languages like Czech permit free word order, while others like English do not? We address this question by pretraining transformer language models on a spectrum of synthetic word-order variants of natural languages. We observe…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…

We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big…

We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then…

Word embeddings are powerful representations that form the foundation of many natural language processing architectures, both in English and in other languages. To gain further insight into word embeddings, we explore their stability (e.g.,…

With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in…

A generalized lexicographic order on words is a lexicographic order where the total order of the alphabet depends on the position of the comparison. A generalized Lyndon word is a finite word which is strictly smallest among its class of…

Words unknown to the lexicon present a substantial problem to part-of-speech tagging. In this paper we present a technique for fully unsupervised statistical acquisition of rules which guess possible parts-of-speech for unknown words. Three…

Existing works have studied the impacts of the order of words within natural text. They usually analyze it by destroying the original order of words to create a scrambled sequence, and then comparing the models' performance between the…

The sound inventories of the world's languages self-organize themselves giving rise to similar cross-linguistic patterns. In this work we attempt to capture this phenomenon of self-organization, which shapes the structure of the consonant…

The order of `noun and adposition' is the important parameter of word ordering rules in the world's languages. The seven parameters, `adverb and verb' and others, have a strong dependence on the `noun and adposition'. Japanese as well as…