Short lists with short programs in short time - a short proof

TL;DR

This paper simplifies and shortens the proof of a result showing that for any string, a polynomial-time algorithm can produce a short list of descriptions, improving understanding of short program generation.

Contribution

The authors provide a simplified and more concise proof of existing results on constructing short description lists in polynomial time.

Findings

Simplified proof of short list construction for string descriptions

Polynomial-time algorithms for generating short descriptions

Enhanced clarity in theoretical understanding of short program lists

Abstract

Bauwens, Mahklin, Vereshchagin and Zimand [ECCC TR13-007] and Teutsch [arxiv:1212.6104] have shown that given a string x it is possible to construct in polynomial time a list containing a short description of it. We simplify their technique and present a shorter proof of this result.