From my understanding, Algorithmic information theory (AIT) gives some ways to define the amount of « structure » in a string: for example sophistication or logical depth (see for instance ), can be used to characterize strings that are complex not because of some trivial randomness, but rather because they are generated by complex programs (plus some possible additional randomness but the non-random part is important).
I’m wondering if it would be possible to use those concepts to detect an intelligent species in space, and if so, has it been done? (For instance in initiatives like Breakthrough Listen ?)
I’m aware some researchers like Laurance R. Doyle are applying information theory to detect, for instance, Zipf’s law patterns in signals (which humans as well as animals like dolphins are shown to exhibit when communicating) , but I’m wondering if there were areas of research looking at the AIT side. For example, we would look at a radio signal (but also possibly a Hubble image, etc...) and compute (an approximation of) its sophistication or logical depth: if it is high then there are a lot of chances that an intelligent specie was involved in its generation process.
But first of all, as a sanity check, on human data vs natural data, would it work? Is there any experiment about this? For instance, is an image of a rock or a cloud less sophisticated than say an image of a motorcycle? Or is there something more that is needed to make it work?
I’m not familiar yet with the theory of sophistication and logical depth because they are quite hard for me to grasp, (although I'm eager to learn), but I was curious about a general high-level idea of what could be possible.
PS: apologies if my question is not precise enough, I'll refine it as needed, but I think as of now it gathers all of the important parts of the question
 Relativity of Depth and Sophistication https://arxiv.org/pdf/2002.06709.pdf