The Maximal Subword Complexity of Quasiperiodic Infinite Words

TL;DR

This paper precisely estimates the maximal subword complexity of quasiperiodic infinite words by representing these words through a finite suffix code derived from their quasiperiod, combining formal language theory and complexity analysis.

Contribution

It introduces a novel representation of quasiperiodic words using a finite suffix code with bounded delay, enabling exact subword complexity estimation.

Findings

Exact maximal subword complexity estimate for quasiperiodic infinite words

Representation of quasiperiodic words via a finite suffix code

Demonstration that the suffix code has bounded delay of decipherability

Abstract

We provide an exact estimate on the maximal subword complexity for quasiperiodic infinite words. To this end we give a representation of the set of finite and of infinite words having a certain quasiperiod q via a finite language derived from q. It is shown that this language is a suffix code having a bounded delay of decipherability. Our estimate of the subword complexity now follows from this result, previously known results on the subword complexity and elementary results on formal power series.