Numeration-automatic sequences

TL;DR

This paper introduces a class of automata that generate numeration systems and provides algorithms for retrieving the n-th word in their language based on the automaton's induced numeration, including reverse reading and automata combination methods.

Contribution

It presents a new class of automata for numeration systems and algorithms for word retrieval, reverse reading, and automata combination, expanding automata-based numeration theory.

Findings

Algorithms for n-th word retrieval in automata-induced numeration systems

Methods for reverse reading of automaton expansions

Techniques for combining automata with similar properties

Abstract

We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton. Furthermore we give some algorithms for reverse reading of this expansion and a way to combine automata to other automata having the same properties.