I just had to contribute to this interesting topic, but I don't care if nobody reads it
Bill819 && Hollywood1
Assuming you are both referring to Neural Networks (spelling really is atrocious on this forum), no they do not dream. In fact they have no intelligence whatsoever as just like Bill819 said it takes input and compares it to what it has been "taught". This is actually even less intelligent then one might think however as a Neural Network simply takes an input (usually a number) and passes it through each layer based upon a set of rules (ie. if NUMBER > 10 pass to neuron A3) and then that neuron does a very simple calculation most often involving a single addition, subtraction, or multiplication, but it can be something more complicated. Then once that calculation is done the result is passed to the next layer of the Neural Network until it reaches the end and the answer is output. As far as I'm aware no Neural Networks in use today use any external information within the network layers so it is limited to only doing things like math or physics computation. In Grand Turismo 4 a Neural Network was used to actually drive the cars as it was given the cars current position and movement and it would output the required movement to stay on the track or the driving line. This is of course quite useful, but what makes Neural Networks particularly "stupid" as compared to Hal is that all it does is a series of boolean logic checks to decide what to do and a Neural Network can be over-trained so that a given range of inputs will always give a specific output when the desired result is a separate output for every input.
As far as making hal Self-Aware or at least appear to be, that would require Hal to keep a buffer of X-number of previous messages and checking each of those against your message before it replies, which even though it could give some wonderful results, could also confuse Hal as to what your responding to and the computations to decide what to respond could be rather slow. I'm not exactly an Academic A.I. expert and my knowledge is more based around it's use in video games where speed and illusion of accuracy is more important then accuracy and actual intelligence. As soon as I've had time to fully understand how Hal's brain works and the scripting therein I have quite a bit planned for making it appear more aware as long as what I have planned is possible within the scripts.
EDIT: Actually if you think of dreaming as the way the brain learns from its experiences, a Neural Network does dream, except it does it backwards. Rather then dreaming about what it has experienced it instead begins its existence with a constant few weeks or months of dreaming and then assuming it passes its tests afterwards it never dreams again. If however, it fails its tests it either goes back to dreaming or it gets wiped out and starts life all over again with some more intensive dreaming.
