Automatic sequences: from rational bases to trees

02/22/2021
by   Michel Rigo, et al.
0

The nth term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of n in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration system with a regular numeration language, we consider these built on languages associated with trees having periodic labeled signatures and, in particular, rational base numeration systems. We obtain two main characterizations of these sequences. The first one is concerned with r-block substitutions where r morphisms are applied periodically. In particular, we provide examples of such sequences that are not morphic. The second characterization involves the factors, or subtrees of finite height, of the tree associated with the numeration system and decorated by the terms of the sequence.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/31/2021

Revisiting regular sequences in light of rational base numeration systems

Regular sequences generalize the extensively studied automatic sequences...
05/19/2020

Decidability and k-Regular Sequences

In this paper we consider a number of natural decision problems involvin...
01/12/2016

Factorization of C-finite Sequences

We discuss how to decide whether a given C-finite sequence can be writte...
02/21/2018

A New Foundation for Finitary Corecursion and Iterative Algebras

This paper contributes to a theory of the behaviour of "finite-state" sy...
12/09/2020

Regular sequences and synchronized sequences in abstract numeration systems

The notion of b-regular sequences was generalized to abstract numeration...
06/13/2021

A Phylogenetic Trees Analysis of SARS-CoV-2

One regards spaces of trees as stratified spaces, to study distributions...
10/07/2019

Gröbner bases for staged trees

In this article we consider the problem of finding generators of the tor...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.