It has recently been shown that no one-dimensional, two-state cellular
automaton can classify binary strings according to whether their dens
ity of Is exceeds 0.5 or not. We show that by changing the output spec
ification, namely, the final pattern toward which the system should co
nverge, without increasing its computational complexity, a two-state,
r = 1 cellular automaton exists that can perfectly solve the density p
roblem.