Work

Automatic Abelian Complexities of Parikh-Collinear Fixed Points

Year: 2024

Type: article

Abstract: Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference DLT–WORDS 2023 we showed that fixed points of Parikh-collinear morphisms are automatic. We also showed that the abelian complexity function of a binary fixed point of such a morphism is automatic under some assumptions. In this note, we fully generalize the latter result. Namely, we show that the abelian complexity function of a fixed point of an arbitrary, possibly erasing, Parikh-collinear morphism is automatic. Furthermore, a deterministic finite automaton with output generating this abelian complexity function is provided by an effective procedure. To that end, we discuss the constant of recognizability of a morphism and the related cutting set.

Source: Theory of Computing Systems

DOI: 10.1007/s00224-024-10197-5

Authors: Michel Rigo, Manon Stipulanti, Markus A. Whiteland

Institutions: University of Liège, Loughborough University

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Fonds De La Recherche Scientifique - FNRS, Université de Liège