A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations
Combinatorics
2024-11-25 v5 Formal Languages and Automata Theory
Abstract
In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and -regular sequences (in the sense of Allouche and Shallit) via their linear representations. In particular, we show that the minimisation algorithm for recognisable series can also be used to minimise linear representations of -regular sequences.
Keywords
Cite
@article{arxiv.2201.13446,
title = {A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations},
author = {Clemens Heuberger and Daniel Krenn and Gabriel F. Lipnik},
journal= {arXiv preprint arXiv:2201.13446},
year = {2024}
}