Work

Quasi-fixed points of substitutive systems

Year: 2025

Type: article

Abstract: We study automatic sequences and automatic systems generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most sequences within an automatic system are not themselves automatic. We provide a complete and succinct classification of automatic sequences that lie in a given automatic system in terms of the quasi-fixed points of the substitution defining the system. Our result extends to factor maps between automatic systems and highlights arithmetic properties underpinning these systems. We conjecture that a similar statement holds for general nonconstant length substitutions.

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2025.104282

Author: Elżbieta Krawczyk

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: $3,560

Funder: Narodowe Centrum Nauki

Award: G319460560