No dice. Kolmogorov complexity is critically dependent on the encoding scheme you use for the complexity measure, and given the nature of the problems in question that's going to really not work. If your encoding scheme favors polynomials but makes expression squares a royal pain, you're going to get a radically different K-complexity number than you will if your encoding goes the other way around. And coming up with both such encodings is trivial.
This is why proofs using K-complexity (forgive me, I often misspell it) always use it in a way that doesn't involve actually assigning numbers to the K-complexity; while it has certain desirable properties, there is no unique K-complexity value for a given language.
Aaaaand it's exactly this reason I also loathe those questions. It is much less "do this mathematical thing" than "read the puzzle-maker's mind", and quite frequently there is simply literally not enough information in the sequence to read the puzzle-makers mind. With an uncountably infinite number of functions to choose from and a finite set of inputs to choose among them, it's a complete joke of a test. On the other hand, with suitable constraints given in advance it could prove quite useful. (... but that would remove the thrill of lording the answer over people, methinks, which I think is a distressingly large part of such problem's appeal....)
> you're going to get a radically different K-complexity number than you will if your encoding goes the other way around.
in the limit, all schemes are roughly equivalent. (they are equivalent up to constants.)
> given the nature of the problems in question that's going to really not work
ok. so attempting to compute the kolmogorov complexity for iq test problems is a bad idea. it isnt actually a computable function. its existence shows there is a mathematically rigorous way to talk about the most plausible way to extend an integer sequence. more than anything, this is a counter to the argument that "an uncountably infinite number of functions to choose from and a finite set of inputs to choose among them" makes the test entirely subjective.
> there is no unique K-complexity value for a given language.
for any given language, there is, unless i dont understand what youre saying.
> your encoding scheme favors polynomials but makes expression squares a royal pain
i know its wrong, but i cant help pointing out that that doesnt actually make any sense at all
This is why proofs using K-complexity (forgive me, I often misspell it) always use it in a way that doesn't involve actually assigning numbers to the K-complexity; while it has certain desirable properties, there is no unique K-complexity value for a given language.
Aaaaand it's exactly this reason I also loathe those questions. It is much less "do this mathematical thing" than "read the puzzle-maker's mind", and quite frequently there is simply literally not enough information in the sequence to read the puzzle-makers mind. With an uncountably infinite number of functions to choose from and a finite set of inputs to choose among them, it's a complete joke of a test. On the other hand, with suitable constraints given in advance it could prove quite useful. (... but that would remove the thrill of lording the answer over people, methinks, which I think is a distressingly large part of such problem's appeal....)