Complexity of Substitutive Sequences - Calculation of the Complexities of Substitutive Sequences Over a Binary Alphabet

TL;DR

This paper investigates the complexity of substitutive sequences over a binary alphabet, deriving a recurrence formula based on initial values and the characteristic polynomial to fully determine their complexity.

Contribution

It introduces a method to compute the complexity of substitutive sequences using recurrence relations derived from the characteristic polynomial.

Findings

Complexity can be expressed via a recurrence formula.

Initial values and characteristic polynomial determine the complexity.

Method applies to various types of special words.

Abstract

We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula determined by the characteristic polynomial.