Bispecial factors in circular non-pushy D0L languages

TL;DR

This paper introduces an algorithmic method to identify bispecial factors in fixed points of non-pushy circular D0L-systems and establishes their equivalence with systems having finite critical exponent.

Contribution

It provides a novel, simple algorithm for finding bispecial words in non-pushy circular D0L-systems and proves their characterization via finite critical exponent.

Findings

Algorithm for finding bispecial words in non-pushy circular D0L-systems

Characterization of these systems as having finite critical exponent

Establishment of a precise link between bispecial factors and system properties

Abstract

We study bispecial factors in fixed points of morphisms. In particular, we propose a simple method of how to find all bispecial words of non-pushy circular D0L-systems. This method can be formulated as an algorithm. Moreover, we prove that non-pushy circular D0L-systems are exactly those with finite critical exponent.