The complexity of evaluating integers and polynomials is studied. A new model is proposed for studying such complexities. This model differs from previous models by requiring the construction of constant to be used in the computation. This construction is given a cost which is dependent upon the size of the constant. Previous models used a uniform cost, of either 0 or 1, for operations involving constants. Using this model, proper hierarchies are shown to exist for both integers and polynomials with respect to evaluation cost. Furthmore, it is shown that almost all integers (polynomials) are as difficult to evaluate as the hardest integer (polynomial). These results remain true even if the underlying basis of binary operations which the algorithm performs are varied.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)