[Note: this webpage last modified Friday, 04-Feb-2011 19:44:51 EST]
Something cool about theory of computing, something you can do with it...
Or, is there a problem in the book you'd like to talk about?
Today's attendance.
Administrative...
Homework 4 will be sent out tonight, model solutions for HW3 will be handed out on Friday.
First exam next Friday, September 24, sample exam and topics list will be handed out on Monday.
Today: hierarchy for NP-type problems. Note that the proof we did last time for regular algorithms/machines does not work because as far as we know NP is not closed under complement. That proof basically was "pick an input for each machine, do the opposite as long as the other machine does not use too much time." Since doing the opposite of an NP-type algorithm cannot be done with an NP-type algorithm (as far as we know), we need to do something else.
So, instead we do delayed diagonalization. Basically, do the complementation on very large "padded input" and then use a copying scheme to copy that complementation down to smaller and smaller padded inputs until it gets to the original input we were interested in in the first place. This goes by way of contradiction - assume the other machine does the same as we do, then this along the construction copies the complementary value all the way to the original input.
See the book for more details...
Next time: maybe another NP-completeness proof.