That model's phase space is about 2000 bits, realistically speaking its behavior never repeats. It can't be searched either, our computational limit today is about 70 bits.
I'm not clear what you're saying there. You shouldn't need to exhaust the phase space to check if the model exhibits a particular behaviour, but perhaps you're not claiming that?
The simulation derives behavior from the state of neural network, in order to produce desired behavior the state should be known first, in general case you need to search it if you don't have a reliable method to reach it from any other state.
