Does K-complexity == Kolmogorov complexity?

Yes, that was my intention.

I am interested what you want to know about these for.

I didn't say I want to know about them. I said I would like to see tutorials so that other people commenting here would know something about them. :)

Like many things, I think a partial understanding of these topics can be counterproductive. (In other words, to be productive I think such posts should be as technical as necessary to get to the level of actually using the concept to solve problems.)

Yes, partial understanding is counter-productive. But it already exists. For example, I mentioned both K-complexity and computational complexity. What do they have in common? Practically nothing! But I've seen evidence that this is not really understood by all LW commenters. I would like to see presentations that are as technical as necessary to show that they are different concepts dealing with different problems.

As for getting to the technical level necessary to solve problems - well, has the concept of Kolmogorov or Chaitin complexity ever really solved a problem, rather than just clarifying a concept?