1IECL - Institut Élie Cartan de Lorraine (Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex
Ile du Saulcy - 57 045 Metz Cedex 01 - France)
Abstract : 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.
https://hal.inria.fr/hal-01824876
Contributor : Hal Ifip
<>
Submitted on : Wednesday, June 27, 2018 - 4:37:58 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:25 PM
Long-term archiving on: Thursday, September 27, 2018 - 3:08:34 AM
File
Restricted access
To satisfy the distribution rights of the publisher, the document is embargoed
until : 2021-01-01
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⟩