Related papers: Topological Entropy of Formal Languages
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we…
Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras, connections to random matrix theory and a discussion of open problems.
Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
In this study, the output of large language models (LLM) is considered an information source generating an unlimited sequence of symbols drawn from a finite alphabet. Given the probabilistic nature of modern LLMs, we assume a probabilistic…
We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…
The maximum entropy method has recently been successfully introduced to a variety of natural language applications. In each of these applications, however, the power of the maximum entropy method is achieved at the cost of a considerable…
This paper introduces an objective metric for evaluating a parsing scheme. It is based on Shannon's original work with letter sequences, which can be extended to part-of-speech tag sequences. It is shown that this regular language is an…
We study the entropy of Chinese and English texts, based on characters in case of Chinese texts and based on words for both languages. Significant differences are found between the languages and between different personal styles of debating…
In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy class. The topological entropy of this graph representative…
We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…
We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…
In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
Using the idea of local entropy theory, we characterize the sequence entropy tuple via mean forms of the sensitive tuple in both topological and measure-theoretical senses. For the measure-theoretical sense, we show that for an ergodic…
An interesting line of research in natural language processing (NLP) aims to incorporate linguistic typology to bridge linguistic diversity and assist the research of low-resource languages. While most works construct linguistic similarity…
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…