Construction of Some Nonautomatic Sequences by Cellular Automata - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2018

Construction of Some Nonautomatic Sequences by Cellular Automata


It is known that if p is a prime number, the columns of linear CA are p-automatic sequences and all p-automatic sequences can be realized by some linear CA with memory. We give some constructions of (nonlinear) CA that realize certain nonautomatic sequences. First, we show through a recoding that from a construction with additional symbols, we can construct a CA using only the symbols occurring in the sequence. This answers a question posed by Rowland and Yassawi. Then, we propose a construction for the characteristic sequence of the integer polynomials, which are nonautomatic sequences by the Minsky–Papert criterion. We also provide a construction based on the indicator of Fibonacci numbers for the Fibonacci word, which is an emblematic nonautomatic sequence.
Fichier principal
Vignette du fichier
469010_1_En_9_Chapter.pdf (310.45 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01824876 , version 1 (27-06-2018)





Irène Marcovici, Thomas Stoll, Pierre-Adrien Tahay. Construction of Some Nonautomatic Sequences by Cellular Automata. AUTOMATA 2018 - 24th International Workshop on Cellular Automata and Discrete Complex Systems, Jun 2018, Ghent, Belgium. pp.113-126, ⟨10.1007/978-3-319-92675-9_9⟩. ⟨hal-01824876⟩
189 View
182 Download



Gmail Facebook X LinkedIn More