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Automaticity of double sequences generated by one-dimensional linear cellular automata
 

Summary: Automaticity of double sequences generated by one-dimensional
linear cellular automata
J.-P. Allouche, F. von Haeseler
, H.-O. Peitgen, A. Petersen§
, G. Skordev
Abstract We give a complete answer to the question whether a double sequence that is gen-
erated by a one-dimensional linear cellular automaton, and whose states are integers modulo m, is
k-automatic or not.
1 Introduction
Can the infinite double sequence generated by a linear one-dimensional cellular automaton whose
values are integers modulo m be produced by a two-dimensional finite automaton? Recall that a
linear one-dimensional cellular automaton can be defined by a polynomial R(X). The configuration
at time t is given by the coefficients of the polynomial R(X)t. The double sequence generated by
the cellular automaton is the sequence (r(n, t))n,t0 defined by
R(X)t
=
n0
r(n, t)Xn
.
In [12], [13], and [3] this question was addressed for k-Fermat cellular automata, i.e., cellular

  

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

 

Collections: Computer Technologies and Information Sciences