A new kind of complexity

Abstract

A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that instances are easy to compute but if input to the function is vague the description of a function is exponentially complex. This property puts a new light on randomness especially on the random oracle model with a couple of practical examples of random oracle implementation. Consequently, there is a new interesting viewpoint on computational complexity in general.