Computable Model Discovery and High-Level-Programming Approximations to Algorithmic Complexity

TL;DR

This paper explores using a high-level programming language, IMP, to approximate algorithmic complexity more efficiently than traditional low-level models, addressing the uncomputability challenge in program discovery.

Contribution

It introduces a proof of concept demonstrating that high-level languages can better express complex routines and improve approximation of algorithmic complexity.

Findings

High-level IMP language allows more succinct expression of complex routines

Potential for more efficient approximations of algorithmic complexity

Addresses uncomputability in program discovery through a new approach

Abstract

Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however, significantly restricts a wider application of exhaustive methods. Here we present a proof of concept of an approach based on IMP, a high-level imperative programming language. Its main advantage is that conceptually complex computational routines are more succinctly expressed, unlike lower-level models such as Turing machines or cellular automata. We investigate if a more expressive higher-level programming language can be more efficient at generating approximations to algorithmic complexity of recursive functions, often of particular mathematical interest.