A new kind of complexity

TL;DR

This paper introduces a new class of functions characterized by easy computability for precise inputs but exponential complexity for vague inputs, offering fresh insights into randomness and computational complexity.

Contribution

It defines a novel class of functions based on their structural properties and explores their implications for randomness and complexity theory.

Findings

Functions are easy to compute with precise inputs

Vague inputs lead to exponential complexity in description

Provides new perspectives on randomness and the random oracle model

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.