Related papers: Commutative positive varieties of languages
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…
Metrically homogeneous graphs are connected graphs which, when endowed with the path metric, are homogeneous as metric spaces. In this paper we introduce the concept of twisted automorphisms, a notion of isomorphism up to a permutation of…
We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contractions. We classify all commuting unitary representations over…
Most languages use the relative order between words to encode meaning relations. Languages differ, however, in what orders they use and how these orders are mapped onto different meanings. We test the hypothesis that, despite these…
A temporal constraint language is a set of relations that are first-order definable over (Q;<). We show that several temporal constraint languages whose constraint satisfaction problem is maximally tractable are also maximally tractable for…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
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 survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
In single-core processors, concurrency requires that multiple processes be interleaved into a single thread of execution by a scheduler. The language-theoretic operation that corresponds to this is the shuffle of two languages: the set of…
We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.
In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The…
Given a set I of word, the set of all words obtained by the shuffle of (copies of) words of I is naturally provided with a partial order. In [FS05], the authors have opened the problem of the characterization of the finite sets I such that…
The theory of cumulants is revisited in the "Rota way", that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular combinatorial Hopf…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
We study centrality of morphisms in a setting derived from that of a pointed category in which binary products commute with coequalisers. The main results of this paper show that much of the behaviour of central morphisms for unital…
Live languages continuously evolve to integrate the cultural change of human societies. This evolution manifests through neologisms (new words) or \textbf{semantic changes} of words (new meaning to existing words). Understanding the meaning…
Let $S$ be a finite alphabet. An injective word over $S$ is a word over $S$ such that each letter in $S$ appears at most once in the word. We study Boolean cell complexes of injective words over $S$ and their commutation classes. This…