String Attractors of Some Simple-Parry Automatic Sequences

Firstly studied by Kempa and Prezza in 2018 as the unifying idea behind text compression algorithms, string attractors have become a compelling object of theoretical research within the community of combinatorics on words. In this context, they have been studied for several families of finite and infinite words. In this paper, we focus on string attractors of prefixes of particular automatic infinite words (including the famous period-doubling and k-bonacci words) related to simple-Parry numbers. For a subfamily of these words, we describe string attractors of optimal size, while for the rest of them, we provide nearly optimal-size ones. Such a contribution is of particular interest, since in general finding smallest string attractors is NP-hard. This extends our previous work published in the international conference WORDS 2023.