An additively optimal interpreter for approximating Kolmogorov prefix complexity

TL;DR

This paper introduces an interpreter for a programming language aimed at approximating Kolmogorov prefix complexity, analyzing its optimality and comparing it with other models to validate its effectiveness.

Contribution

It presents a new high-level language model for approximating Kolmogorov complexity and evaluates its interpreter's optimality within the Coding Theorem Method framework.

Findings

CTM with this model shows inconsistent correlation with lower-level models.

The model provides a strong correlation with upper bounds of Kolmogorov complexity.

Some models may need larger program spaces to better approximate universal distributions.

Abstract

We study practical approximations to Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the interpreter optimality for this language as the reference machine for the Coding Theorem Method (CTM). A method advanced to deal with applications to algorithmic complexity different to the popular traditional lossless compression approach based on the principles of algorithmic probability. The chosen model of computation is proven to be suitable for this task and a comparison to other models and methods is performed. Our findings show that CTM approximations using our model do not always correlate with results from lower-level models of computation. This suggests some models may require a larger program space to converge to Levin's universal distribution. Furthermore, we compare CTM with an upper bound to Kolmogorov complexity and find a strong correlation, supporting CTM's validity as an approximation method with finer-grade resolution of K.