Nonetheless, \(\mathfrak{P}\) is a useful theoretical model in that it provides a formal medium for implementing procedures which call for certain operations to be carried out simultaneously in parallel. g. , Papadimitriou 1994). But this observation would still be of little practical significance if the algorithms in question achieved such speed up only at the cost of having to employ exponentially many processors relative to the size of their inputs. For in this case it seems that we would hav