Comment on "Some non-conventional ideas about algorithmic complexity"

TL;DR

This paper clarifies a misconception about algorithmic complexity, demonstrating that a list can contain a string with higher complexity than the list itself when the definition is properly applied.

Contribution

It provides a correct interpretation of algorithmic complexity in response to a controversial claim, resolving apparent paradoxes.

Findings

The statement by D'Abramo is not paradoxical when properly understood.

Proper application of algorithmic complexity definitions clarifies the issue.

The paper refutes the misconception about complexity bounds in lists.

Abstract

We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater than that of the entire list. We show that this statement, although perplexing, is not as paradoxical as it seems when the definition of algorithmic complexity is applied correctly.