Check it out.
Here's another one.
I suppose I should say a word or two to get you to click. Both involve automata and probability, but in rather different ways. I know the suspense must be killing you by now -- all the answers are only a click away!..
UPDATE II: That first paper has a mistake, discovered by Dana Angluin and Lev Reyzin. It has been pulled from submission. The mistake seems fixable and possibly already fixed. Developing...
UPDATE III: (Dec. 13, 2009) A new paper is up by Dana Angluin, David Eisenstat, Lev Reyzin and yours truly. Among other results, it shows that learning DFAs in the way I suggested (by sampling random ones and invoking AdaBoost) is impossible since one can embed parity in random DFAs.