## Archive for October 21st, 2009

### A conversation about complexity lower bounds, VII

October 21, 2009

Another somewhat inconclusive instalment, but it introduces another candidate for a non-natural property that might be of some use. (In a later instalment, a heuristic argument is proposed that would show, if correct, that in fact it is not of any use …)

*****************************************

8) What’s on the agenda for today?

🙂 Well, there are two main things I’d like to discuss. One is our “proof” that a random low-complexity function was indistinguishable from a purely random function if you use anything $U^k$-ish to do the distinguishing. I have a small problem with the argument, though I wouldn’t go so far as to say that it is wrong.

The second is that we haven’t got round to having a serious discussion of the lessons that can be drawn from the failure of the approach. If it’s true that it doesn’t work, then I think we can come up with a pretty general class of “simplicity properties” that fail for similar reasons. But I’d like to be as precise about that as possible. (more…)