On Function Description

TL;DR

This paper explores the categorization of function descriptions using computational methods, revealing implications for complexity theory and the Random Oracle Model, and challenging traditional notions of object complexity.

Contribution

It introduces a new perspective on function description categorization and its impact on foundational complexity concepts and models.

Findings

Function descriptions can be categorized into at least two types.

The categorization affects the understanding of Kolmogorov complexity.

Implications for the Random Oracle Model are discussed.

Abstract

The main result is that: function descriptions are not made equal, and they can be categorised in at least two categories using various computational methods for function evaluation. The result affects Kolmogorov complexity and Random Oracle Model notions. More precisely, the idea that the size of an object and the size of the smallest computer program defining that object is a ratio that represents the object complexity needs additional definitions to hold its original assertions.