If I'm correct, some boolean formulas in CNF require exponential size when being converted to an equivalent DNF version (and vice versa).
But what is an example of such a formula (and is there a general way to capture their structure - if the first question is too easy, and I'm just too stupid to see it)?
In this post, the parity function is discussed as an example of a function which blows up exponentially when converted to both CNF and DNF from a non-NF version: Formulas for which any equivalent CNF formula has exponential length
But what about just CNF <=> DNF? And how frequent are these "bad" formulas? (Very rare, I'd suspect, but can it be proved?)