Related papers: Mapping words to powers by morphisms
We provide the first examples of words in the free group of rank 2 which are not proper powers and for which the corresponding word maps are non-surjective on an infinite family of finite non-abelian simple groups.
A power-free language is characterized by the number of symbols used and a limit on how many times a block of symbols can repeat consecutively. For certain values of these parameters, it is known that the number of legal words grows…
In testing the independence of two Gaussian populations, one computes the distribution of the sample canonical correlation coefficients, given that the actual correlation is zero. The "Laplace transform" of this distribution is not only an…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…
Grammatical inference consists in learning a language or a grammar from data. In this paper, we consider a number of models for inferring a non-deterministic finite automaton (NFA) with 3 sorts of states, that must accept some words, and…
We investigate the computational power of periodically iterated morphisms, also known as D0L systems with periodic control, PD0L systems for short. These systems give rise to a class of one-sided infinite sequences, called PD0L words. We…
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…
In the era of deep learning, word embeddings are essential when dealing with text tasks. However, storing and accessing these embeddings requires a large amount of space. This is not conducive to the deployment of these models on…
Morphic words are letter-to-letter images of fixed points $x$ of morphisms on finite alphabets. There are situations where these letter-to-letter maps do not occur naturally, but have to be replaced by a morphism. We call this a decoration…
In this paper we study the asymptotic behaviour of two relatively new complexity functions defined on infinite words and their relationship to periodicity. Given a factor $u$ of an infinite word $x$, we say $u$ is closed if it is a letter…
We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are…
Understanding what knowledge is implicitly encoded in deep learning models is essential for improving the interpretability of AI systems. This paper examines common methods to explain the knowledge encoded in word embeddings, which are core…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
We consider polynomial maps described by so-called "(multivariate) linearized polynomials". These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
We consider the language consisting of all words such that it is possible to obtain the empty word by iteratively deleting powers. It turns out that in the case of deleting squares in binary words this language is regular, and in the case…
Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in…
Word embeddings are a powerful natural language processing technique, but they are extremely difficult to interpret. To enable interpretable NLP models, we create vectors where each dimension is inherently interpretable. By inherently…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…