A1 Refereed original research article in a scientific journal
On the trace subshifts of fractional multiplication automata
Authors: Kopra Johan
Publisher: ELSEVIER
Publication year: 2021
Journal: Theoretical Computer Science
Journal name in source: THEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Volume: 851
First page : 92
Last page: 110
Number of pages: 19
ISSN: 0304-3975
eISSN: 1879-2294
DOI: https://doi.org/10.1016/j.tcs.2020.11.010
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/51286958
Abstract
We address the dynamics of the cellular automaton (CA) that multiplies by p/q in base pq (for coprime p > q > 1) by studying its trace subshift. We present a conjugacy of the trace to a previously studied base-p/q numeration system. We also show that the trace subshift is not synchronizing and in particular not sofic. As a byproduct we compute its complexity function and we conclude by presenting an example of a sofic shift with the same complexity function.
We address the dynamics of the cellular automaton (CA) that multiplies by p/q in base pq (for coprime p > q > 1) by studying its trace subshift. We present a conjugacy of the trace to a previously studied base-p/q numeration system. We also show that the trace subshift is not synchronizing and in particular not sofic. As a byproduct we compute its complexity function and we conclude by presenting an example of a sofic shift with the same complexity function.
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