Related papers: On certain recurrent and automatic sequences in fi…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Sequences with {\em perfect linear complexity profile} were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently {\em apwenian sequences}, first with values $\pm 1$, then with values…
Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is…
We make certain bounds in Krebs' proof of Cobham's theorem explicit and obtain corresponding upper bounds on the length of a common prefix of an aperiodic $a$-automatic sequence and an aperiodic $b$-automatic sequence, where $a$ and $b$ are…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
Venkatachala on the one hand, and Avdispahi\'c & Zejnulahi on the other, both studiied integer sequences with an unusual sum property defined in a greedy way, and proved many results about them. However, their proofs were rather lengthy and…
We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on…
Given an algebraically closed field $K$, a dynamical sequence over $K$ is a $K$-valued sequence of the form $a(n):= f(\phi^n(x_0))$, where $\phi\colon X\to X$ and $f\colon X\to\mathbb{A}^1$ are rational maps defined over $K$, and $x_0\in X$…
In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
It is well known that any power series over a finite field represents a rational function if and only if its sequence of coefficients is ultimately periodic. The famous Christol's Theorem states that a power series over a finite field is…
We identify a binary sequence $\mathcal{S}=(s_n)_{n=0}^\infty$ with the $2$-adic integer $G_\mathcal{S}(2)=\sum\limits_{n=0}^\infty s_n2^n$. In the case that $G_\mathcal{S}(2)$ is algebraic over $\mathbb{Q}$ of degree $d\ge 2$, we prove…
We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several…
We obtain a new bound on certain double sums of multiplicative characters improving the range of several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical…
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…
First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…
In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences,…
In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…