Corn stalks in the composter?

My corn is just about finished. Can I cut up the stalks and add them to the composter? Or, do they take forever to break down? If I can use them, are they better if used when green, or should I let them dry out first? Thanks for any input. I'm new at this, but I'm liking it a lot.

If you compost them, they better be in tiny pieces!

I agree with Homers: cut up the stalks into small pieces. I do this with the corn shucks and cobs from our summertime meals. They take a long time to break down, but they eventually do.
As I sift out my compost I just keep throwing the "undigested" pieces back into the compost pile.