String attractors and pseudopalindromic closures

Ľubomíra Dvořáková
Czech Technical University, Prague

Date(s) : 10/10/2023   iCal
15 h 00 min - 16 h 00 min

In this contribution we carry on a study of string attractors of important classes of sequences. Attractors of minimum size of factors/prefixes/particular prefixes of the following sequences have been determined so far: Sturmian sequences (Mantaci, Restivo, Romana, Rosone, Sciortino, 2021, Dvořáková, 2022), episturmian sequences (Dvořáková, 2022), the Tribonacci sequence (Schaeffer and Shallit, 2021), the Thue-Morse sequence (Kutsukake, 2020, Schaeffer and Shallit, 2021, Dolce, 2023), the period-doubling sequence (Schaeffer and Shallit, 2021), the powers of two sequence (Schaeffer and Shallit, 2021, Kociumaka, Navarro, Prezza, 2021), complementary-symmetric Rote sequences (Dvořáková and Hendrychová, 2023). Recently, string attractors in fixed points of k-bonacci-like morphisms have been described (Gheeraert, Romana, Stipulanti, 2023).

In our talk we aim to present the following results: Using the fact that standard Sturmian sequences may be obtained when iterating palindromic closure, we were able to find attractors of minimum size of all factors of Sturmian sequences. These attractors were different from the ones found for prefixes by Mantaci et al. It was then straightforward to generalize the result to factors of episturmian sequences. Observing usefullness of palindromic closures when dealing with attractors, we turned our attention to pseudopalindromic prefixes of the so-called binary generalized pseudostandard sequences. We determined the minimum size attractors in two cases: for pseudostandard sequences obtained when iterating uniquely the antipalindromic closure (the minimum size is three) and for the complementary-symmetric Rote sequences when iterating both palindromic and antipalindromic closure (the minimum size is two).

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