# An Additively Optimal Interpreter for Approximating Kolmogorov Prefix Complexity

## TL;DR

This paper explores a new method for approximating algorithmic complexity using a high-level programming language interpreter, showing it provides better resolution than traditional approaches.

## Contribution

The paper introduces an additively optimal interpreter for the Coding Theorem Method, improving the approximation of Kolmogorov complexity.

## Key findings

- CTM approximations using the proposed model do not always align with lower-level computation models.
- The CTM shows strong correlation with an upper bound on Kolmogorov complexity, validating its effectiveness.
- Some models may need larger program spaces to converge to Levin’s universal distribution.

## Abstract

We study practical approximations of Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Method (CTM). This method is designed to address applications of algorithmic complexity that differ from 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 conducted. Our findings show that CTM approximations using our model do not always correlate with the results from lower-level models of computation. This suggests that some models may require a larger program space to converge to Levin’s universal distribution. Furthermore, we compare the CTM with an upper bound on Kolmogorov complexity and find a strong correlation, supporting the CTM’s validity as an approximation method with finer-grade resolution of K.