Synchronizing delay for binary uniform morphisms

TL;DR

This paper introduces a graph-based tool to determine the minimal synchronizing delay in circular D0L-systems with binary uniform morphisms, providing a general upper bound for such delays.

Contribution

The paper presents the graph of overhangs as a novel method to analyze and bound the synchronizing delay in circular D0L-systems with binary uniform morphisms.

Findings

Graph of overhangs effectively finds minimal synchronizing delay

Established a general upper bound for binary uniform morphisms

Enhanced understanding of circular D0L-system synchronization

Abstract

Circular D0L-systems are those with finite synchronizing delay. We introduce a tool called graph of overhangs which can be used to find the minimal value of synchronizing delay of a given D0L-system. By studying the graphs of overhangs, a general upper bound on the minimal value of a synchronizing delay of a circular D0L-system with a binary uniform morphism is given.