On Quasiperiodic Morphisms

TL;DR

This paper investigates weakly and strongly quasiperiodic morphisms, providing algorithms to determine their quasiperiodicity properties on finite and infinite words, thereby advancing the understanding of quasiperiodic word structures.

Contribution

It introduces formal definitions of weakly and strongly quasiperiodic morphisms and develops algorithms to decide their quasiperiodicity on finite and infinite words.

Findings

Algorithms for deciding strong quasiperiodicity on finite words

Algorithms for deciding strong quasiperiodicity on infinite words

Analysis of relations among four families of quasiperiodic morphisms

Abstract

Weakly and strongly quasiperiodic morphisms are tools introduced to study quasiperiodic words. Formally they map respectively at least one or any non-quasiperiodic word to a quasiperiodic word. Considering them both on finite and infinite words, we get four families of morphisms between which we study relations. We provide algorithms to decide whether a morphism is strongly quasiperiodic on finite words or on infinite words.