Hello Pasti,
Well, I don't know much about modeling spacetimes (not my subject). However, the question is if it can be done in principle. If you can formally describe what is going on then that's enough.
Another way to approch this is from the perspective of information theory. I think that Seth Lloyd has done some recent work on that. You could say that assuming the universe is algorithmic in some sense (Seth Lloyd doesn't make such assumptions) then that poses limits on the performance of a computer you can build (you can't compute faster than the universe itself).
It is known that classical mechanics allows for ceretain non-computational phenomena. In a purely Newtonial world you could build a so-called ''Rapidly Accelerating Computer'', that could perform an infinite number of computations in a finite time.
So, according to what we know about the universe, we could be living inside an algorithm.
