Is it indeed the case that the more resources one has, the more one can achieve? The answer may seem obvious, but the obvious answer (of yes) actually presumes that the worker knows what resources are at his/her disposal. In this case, when allocated more resources, the worker (or computation) can indeed achieve more. But otherwise, nothing may be gained by adding resources.

In the context of Computational Complexity, an algorithm knows the amount of resources that it is allocated if it can determine this amount without exceeding the corresponding resources. This condition is satisfied in all “reasonable” cases, but it may not hold in general. The latter fact should not be that surprising: We already know that some functions are not computable, and if these functions are used to determine resources then the algorithm may be in trouble. Needless to say, this discussion requires some formalization, which is provided in the current chapter.