相关论文: Introducing Privileged Words: Privileged Complexit…
The prefix palindromic length $\mathrm{PPL}_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. Since 2013, it is still unknown if…
Selectional preference learning methods have usually focused on word-to-class relations, e.g., a verb selects as its subject a given nominal class. This papers extends previous statistical models to class-to-class preferences, and presents…
A word is called closed if it has a prefix which is also its suffix and there is no internal occurrences of this prefix in the word. In this paper we study words that are rich in closed factors, i.e., which contain the maximal possible…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We introduce generalizations of powers and factor complexity via orbits of group actions. These generalizations include concepts like abelian powers and abelian complexity. It is shown that this notion of factor complexity cannot be used to…
We consider rotations on the torus $\mathbb{T}^2$, and we classify them with respect to the complexity functions. In dimension one, a minimal rotation can be coded by a sturmian word. A sturmian word has complexity $n+1$ by the…
The prefix palindromic length $p_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. This function is surprisingly difficult to…
We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope $\alpha$, there exists exactly six minimal squares in its language (a minimal square does not have a square as a proper prefix). A…
Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness,…
In this study, we employ a classification approach to show that different categories of literary "quality" display unique linguistic profiles, leveraging a corpus that encompasses titles from the Norton Anthology, Penguin Classics series,…
We characterize binary words that have exactly two unbordered conjugates and show that they can be expressed as a product of two palindromes.
An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain at most $\Theta(n^2)$ distinct factors, and there exist words of length $n$ containing $\Theta(n^2)$ distinct…
Let us consider an infinite word and $k\geq 1$ an integer. By steps of $k$, we substitute a letter ofthis infinite word by the power of an external letter. The new word obtaining by this process is called $k$ to $k$ substitution of a power…
Modern natural language understanding models depend on pretrained subword embeddings, but applications may need to reason about words that were never or rarely seen during pretraining. We show that examples that depend critically on a rarer…
We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language…
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…
We give a combinatorial definition of the second parameter describing Sturmian words, that we call formal intercept, as an infinite Ostrowski expansion. We recall the well-known properties of Sturmian words, study factors graphs and…
One of the major benefits of belonging to a prestigious group is that it affects the way you are viewed by others. Here I use a simple mathematical model to explore the implications of this "prestige bias" when candidates undergo repeated…
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…
We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of distinct sums exhibited by factors of the same length is bounded…