tl;dr: Simply put, if a computing system the size of, for example, a hundred petabits cannot compress an arbitrarily large amount of data, then there is no point in looking for consciousness in it.

I read an article by the philosopher Dubrovsky in which he had the courage to propose a solution to the so-called "Hard problem of consciousness". Unfortunately, like all the “solutions” to this problem that I have come across, this article does not offer a constructive way to determine whether a computing system has consciousness. However, most of these articles are written by philosophers, and philosophers’ ideas about calculations and proofs do not go beyond the multiplication table and the Pythagorean theorem.

There is, however, a method recognized by the scientific community as constructive. This is a Turing test: testing a certain system for the presence of consciousness with the help of other carriers of consciousness. Without them the test will not work. Well, it doesn’t work anyway, as the experiments show (unless, of course, you believe that the programs tested have consciousness).

Instead of the Turing test, I would propose a test for Kolmogorov complexity. If the system under test has a complexity greater than Kolmogorov's, then it may be conscious. Although the “Kolmogorov test” is not sufficient, it is still more economical than the Turing test since at least it does not require other consciousnesses as testing tools.

This is the size of the resources required to compress some data using some formal language. Complexity greater than Kolmogorov's means the ability of an algorithm to compress the same data using fewer resources (which is formally impossible like conscious computations). The difficulty of calculating the Kolmogorov complexity can be avoided by choosing as a measure of this complexity a certain (obviously insufficient to save large data) constant.

ps https://urlday.cc/s8uq5 (dubrovsky article)