The Reachability of Computer Programs

TL;DR

This paper explores the concept of program reachability as a probability function based on the energetic cost of problems, aiming to understand the emergence of new algorithms through a mathematical lens.

Contribution

It introduces the novel idea of analyzing the discovery of algorithms using a probabilistic framework tied to algorithmic entropy.

Findings

Defines program reachability as a probability function.

Links the emergence of algorithms to energetic cost measures.

Provides a new perspective on algorithm discovery processes.

Abstract

Would it be possible to explain the emergence of new computational ideas using the computation itself? Would it be feasible to describe the discovery process of new algorithmic solutions using only mathematics? This study is the first effort to analyze the nature of such inquiry from the viewpoint of effort to find a new algorithmic solution to a given problem. We define program reachability as a probability function whose argument is a form of the energetic cost (algorithmic entropy) of the problem.