If a parallel algorithm requires exponentially many processors relative to input size, there is little hope of building a computing device on which it could be concretely implemented
A set of computational steps designed to be executed simultaneously across multiple processors or computers working together, rather than one after another on a single processor.
Processors(as used in computer science)
The computing chips or units that actually do the calculations and execute instructions in a computer.
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