  Generation and prediction of time series is analyzed for the case of a
Bit-Generator: a perceptron where in each time step the input units are shifted
one bit to the right with the state of the leftmost input unit set equal to the
output unit in the previous time step. The long-time dynamical behavior of the
Bit-Generator consists of cycles whose typical period scale polynomially with
the size of the network and whose spatial structure is periodic with a typical
finite wave length. The generalization erroron a cycle is zero for a finite
training set and global dynamical behaviors such as the cycle period can also
be learned in a finite time. Hence, a projection of a rule can be learned in a
finite time.
