I could agree with you, in the sense that computational complexity can address some aspect of consciousness, but could be use to hide the conceptual issue.
As they use mechanism, they should better “just" listen to the machine, and what she says about herself.
“Just” is in quote because today that requires the study of Gödel 1931, Turing 1936, Church 1936, Löb 1955, … Solovay 1975 (G and G*).
I don’t remember if you agree with the following quasi-definition of consciousness, which is that “I am conscious”, from the first person point of view of a machine is something verifying the following conditions;
It is immediately known
It is indubitable
It is non provable
It is non definable
The machine has soul, it lives at the intersection of the believable and truth, it is like a inner God, nobody can define it, although everybody can use the indexical “I” to get a local ostensive temporary “not-a-name” but 3p image in the mind of the others.The machine knows that this soul is not just non definable, but she can refute explicitly all effective theories made about her and what she could be.
The Gödel-Löbian machine can destroy effectively all reductionist conception you could have about her.
And that does not need a lot of complexity. Just Robinson Arithmetic (RA, a sub theory of all branches in “exact sciences” if not implicit in most human sciences as well) + the induction axioms (the axioms responsible for the rich cognitive ability. (RA emulates all machines, and I interview the richer Löbian machine that RA emulates. I mean, the induction axioms are not in the ontological part). Arithmetic emulates/enacted relative numbers believing in sets and infinities.
Bruno