Shorter and faster than Sort3AlphaDev

TL;DR

This paper challenges previous claims by presenting shorter and faster sorting algorithm implementations for three numbers, using deep reinforcement learning, and provides counterexamples and optimized C/C++ code.

Contribution

It introduces counterexamples to prior claims of minimal program length and offers a more efficient implementation for sorting three numbers.

Findings

Counterexamples to the claim of minimal 17-instruction program

Faster C/C++ implementation than previous deep RL solutions

Demonstrates that shorter solutions are possible for small input sorting

Abstract

Arising from: Mankowitz, D.J., Michi, A., Zhernov, A. et al. Faster sorting algorithms discovered using deep reinforcement learning.Nature 618, 257-263 (2023). doi.org/10.1038/s41586-023-06004-9. The article cited above presents new implementations of sorting algorithms found through deep reinforcement learning that work on a small number of numeric inputs. For 3 numbers, the published implementation contains 17 assembly instructions, and the authors state that no shorter program exists. This note presents two counterexamples for this claim and a straightforward C/C++ implementation that is faster than theirs.