Related papers: Commutative positive varieties of languages
We study the shifted convolution sum of the divisor function and some other arithmetic functions.
A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation…
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a…
The paper presents an experiment of solving word equations via specialization of a configuration WE(R,E), where the program WE can be considered as an interpreter testing whether a composition of substitutions R produces a solution of a…
We study a standard operator on classes of languages: unambiguous polynomial closure. We prove that for every class C of regular languages satisfying mild properties, the membership problem for its unambiguous polynomial closure UPol(C)…
This study explores language change and variation in Toki Pona, a constructed language with approximately 120 core words. Taking a computational and corpus-based approach, the study examines features including fluid word classes and…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
A systematic way of defining variants of a modeling language is useful for adapting the language to domain or project specific needs. Variants can be obtained by adapting the syntax or semantics of the language. In this paper, we take a…
Large language models (LLMs) often encode word-form variation (e.g., walk vs. walked) as linear directions in the embedding space. However, standard tokenization algorithms treat such variants as distinct words with different vocabulary…
We investigate the least number of palindromic factors in an infinite word. We first consider general alphabets, and give answers to this problem for periodic and non-periodic words, closed or not under reversal of factors. We then…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…
We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
In this work we construct an automaton for the commutative closure of a given regular group language. The number of states of the resulting automaton is bounded by the number of states of the original automaton, raised to the power of the…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
Word embeddings are a powerful approach for unsupervised analysis of language. Recently, Rudolph et al. (2016) developed exponential family embeddings, which cast word embeddings in a probabilistic framework. Here, we develop dynamic…
A generalized word in two letters $A$ and $B$ is an expression of the form $W=A^{\alpha_1}B^{\beta_1}A^{\alpha_2}B^{\beta_2}... A^{\alpha_N}B^{\beta_N}$ in which the exponents $\alpha_i$, $\beta_i$ are nonzero real numbers. When independent…
The human language can be expressed through multiple sources of information known as modalities, including tones of voice, facial gestures, and spoken language. Recent multimodal learning with strong performances on human-centric tasks such…