Related papers: How to prove that a sequence is not automatic
After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…
The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic…
Let $m$ be a positive integer larger than $1$, let $w$ be a finite word over $\left\{0,1,...,m-1\right\}$ and let $a_{m;w}(n)$ be the number of occurrences of the word $w$ in the $m$-expansion of $n$ mod $p$ for any non-negative integer…
First we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutations and p-adic system, and consider the necessary-sufficient condition that it is non-periodic. Moreover if the generalized Thue-Morse…
Congruences for stochastic automata are defined, the correspondin factor automata are constructed and investigated for automata ove analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple…
We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, torsions, generalised torsions and cofinal elements.
In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly…
Nested (or meta-Fibonacci) recurrences, such as the recurrence used to define Hofstadter's Q-sequence, along with the digit-based recurrences that underlie automatic sequences are of interest from both number-theoretic and combinatorial…
Given a one-dimensional shift $X$, let $|F_X(\ell)|$ be the number of follower sets of words of length $\ell$ in $X$. We call the sequence $\{|F_X(\ell)|\}_{\ell \in \mathbb{N}}$ the follower set sequence of the shift $X$. Extender sets are…
In this short note we show that a k-automatic sequence and a Sturmian sequence cannot have arbitrarily large factors in common.
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
We show that functions of type $X_n = P[Z^n]$, where $P[t]$ is a periodic function and $Z$ is a generic real number, can produce sequences such that any string of values $X_{s}, X_{s+1}, ...,X_{s+m}$ is deterministically independent of past…
We investigate the running sums of some well-known automatic sequences to determine whether they are synchronised.
Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of…
The different interpretations of quantum mechanics yield the same experimental results, which may give the impression that the question of what interpretation is the true one, is a philosophical question, not a scientific one. But in this…
The notion of almost periodicity nontrivially generalizes the notion of periodicity. Strongly almost periodic sequences (=uniformly recurrent infinite words) first appeared in the field of symbolic dynamics, but then turned out to be…
Motivated by a question of van der Poorten about the existence of infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen…
The predictability of a sequence is defined as the asymptotic performance of the best performing predictor in a given class. The value of the predictability of a sequence will in general depend on the choice of this predictor class. The…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
We introduce an elementary congruence-based procedure to look for q-th power multiples in arbitrary binary recurrence sequences (q>2). The procedure allows to prove that no such multiples exist in many instances.