 The resources involved in carrying out an algorithm to decide an instance of a problems can typically be measured in terms of the number of processor cycles (i.e. elementary computational steps) and the amount of memory space (i.e. storage for auxiliary calculations) which are required to return a solution.   The methods of complexity theory can be useful not only in deciding how we can most efficiently expend such resources, but also in helping us to distinguish which effectively decidable problems possess efficient decision methods in the first place.  In this regard, it is traditional to distinguish pre-theoretically between the class of feasibly decidable problems  – i.e. those which can be solved in practice by an efficient algorithm – and the class of intractable problems – i.e. those which lack such algorithms and may thus be regarded as intrinsically difficult to decide (despite possibly being decidable in principle). The significance of this distinction is most readily appreciated by considering some additional examples.