Central to the development of computational complexity theory is the notion of a decision problem. Such a problem corresponds to a set \(X\) in which we wish to decide membership. For instance the problem \(\sc{PRIMES}\) corresponds to the subset of the natural numbers which are prime – i.e. \(\{n \in \mathbb{N} \mid n \text{ is prime}\}\). Decision problems are typically specified in the form of questions about a class of mathematical objects whose positive instances determine the set in question – e.g.