  We study the influence of the dimension of cellular automata (CA) for real
time language recognition of one-dimensional languages with parallel input.
Specifically, we focus on the question of determining whether every language
that can be recognized in real time on a 2-dimensional CA working on the Moore
neighborhood can also be recognized in real time by a 1-dimensional CA working
on the standard two-way neighborhood.
  We show that 2-dimensional CA in real time can perform a linear number of
simulations of a 1-dimensional real time CA. If the two classes are equal then
the number of simulated instances can be polynomial.
