What Elman networks cannot do

Finds out properties of Elman networks which are inherent to the architecture. Using methods from control theory a representation for the network is developed, which shows all the capabilities of the network in a very compact form. With this new kind of representation the impact of the different weights is analyzed in detail. A very simple learning task, which seems unsolvable with a given Elman network is analyzed and the developed representation is used to prove that the task cannot be learned. The results of the simple learning task are generalized to networks of any size and for certain learning tasks a lower boundary for the minimum number of hidden units is given.