detalle del documento
IDENTIFICACIÓN
oai:arXiv.org:2405.18032
Tema
Computer Science - Discrete Mathem... Computer Science - Formal Language... Mathematics - CombinatoricsAutor
Rigo, Michel Stipulanti, Manon Whiteland, Markus A.Categoría
Computer Science
Año
2024
fecha de cotización
5/6/2024
Palabras clave
complexity morphisms morphism function automatic abelian fixedResumen
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.
;Comment: 18 pages, 2 figures, long version of [M. Rigo, M. Stipulanti, M. A. Whiteland, Automaticity and Parikh-collinear morphisms.
In: Combinatorics on Words.
Lecture Notes in Comput.
Sci., vol. 13899, pp. 247-260.
Springer, 2023]
Rigo, Michel,Stipulanti, Manon,Whiteland, Markus A., 2024, Automatic Abelian Complexities of Parikh-Collinear Fixed Points
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