String attractors of Rote sequences

TL;DR

This paper investigates minimal string attractors of pseudopalindromic prefixes in Rote sequences, revealing size-two attractors for certain subclasses and proposing a conjecture for a universal bound in generalized pseudostandard sequences.

Contribution

It characterizes minimal string attractors for pseudopalindromic prefixes of Rote sequences and introduces a conjecture on their size bounds.

Findings

Minimal string attractors of size two for standard Sturmian sequences.

Attractors of size three for antipalindromic prefixes of pseudostandard sequences.

Conjecture that all such prefixes have attractors of size at most four.

Abstract

In this paper, we describe minimal string attractors (of size two) of pseudopalindromic prefixes of standard complementary-symmetric Rote sequences. Such a class of Rote sequences forms a subclass of binary generalized pseudostandard sequences, i.e., of sequences obtained when iterating palindromic and antipalindromic closures. When iterating only palindromic closure, palindromic prefixes of standard Sturmian sequences are obtained and their string attractors are of size two. However, already when iterating only antipalindromic closure, antipalindromic prefixes of binary pseudostandard sequences are obtained and we prove that the minimal string attractors are of size three in this case. We conjecture that the pseudopalindromic prefixes of any binary generalized pseudostandard sequence have a minimal string attractor of size at most four.