A4 Refereed article in a conference publication
Symbol Frequencies in Surjective Cellular Automata
Authors: Hellouin de Menibus, Benjamin; Salo, Ville; Törmä, Ilkka
Editors: Riva, Sara; Richard, Adrien
Conference name: International Workshop on Cellular Automata and Discrete Complex Systems
Publisher: Springer Nature Switzerland
Publication year: 2025
Journal: Lecture Notes in Computer Science
Book title : Cellular Automata and Discrete Complex Systems: 31st IFIP WG 1.5 International Workshop, AUTOMATA 2025, Lille, France, June 30 – July 2, 2025, Proceedings
Volume: 15831
First page : 154
Last page: 170
ISBN: 978-3-032-01569-3
eISBN: 978-3-032-01570-9
ISSN: 0302-9743
eISSN: 1611-3349
DOI: https://doi.org/10.1007/978-3-032-01570-9_11
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : No Open Access publication channel
Web address : https://doi.org/10.1007/978-3-032-01570-9_11
We study the behavior of probability measures under iteration of a surjective cellular automaton. We solve the following question in the negative: if the initial measure is ergodic and has full support, do all weak-* limit points of the sequence of measures have full support as well? The initial measure of our solution is not a product measure, and in this case the question remains open. To this end, we present a tool for studying the frequencies of symbols in preimages of surjective cellular automata, and prove some basic results about it. However, we show that by itself it is not enough to solve the stricter question in the positive.
