 
Summary: Automaticity of double sequences generated by onedimensional
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 onedimensional linear cellular automaton, and whose states are integers modulo m, is
kautomatic or not.
1 Introduction
Can the infinite double sequence generated by a linear onedimensional cellular automaton whose
values are integers modulo m be produced by a twodimensional finite automaton? Recall that a
linear onedimensional 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 kFermat cellular automata, i.e., cellular
