If we assume that we have complete knowledge of the state of the entire universe at one instant, plus a total understanding of the systems by which the universe "runs" and matter interacts and what fluctuations occur in these rulings throughout space-time, I don't see any reason why the computer should not be able to predict all things, even the effects of its own predictions.

I think the word you're looking for is "omnipotence"....

Personally the most impressive aspect of attaining that hypothetical situation would be the derivation of a universal theory of everything, whereby you can predict the interactions of all universal matter even if time is "flowing" in another direction at different regions in space-time.

Then again, would the observation be valid if the computer was moved to another location - the laws of momentum are inherently relativistic - everything is in relation to an initial "static" platform from the observer's POV - would the computer predict a different universe 3 metres to the left?

What if it was in motion, or if time's arrow was pointing in the opposite direction?

Probably best left as a hypothetical, perhaps.

Bourne "When science becomes philosophy, Bertrand Russell spins in his grave..."