Jeff's August 27 Class Notes
[Note: this webpage last modified Friday, 04-Feb-2011 19:44:51 EST]
- Today's attendance quiz.
- You should be working on the homework.
- Office hours Monday and Friday 11-noon in my office.
- Tegrity.
- Prereq exam review.
- Overview of things to come.
- P, and some examples of things in P, how you prove something is
in P.
- NP, and some examples, how you prove things are in NP.
- Lots of NP complete problems - if can solve any of them, then
can solve them all (and would also have theorem proving, and would
not have cryptography).
- If allow randomness can do some things we don't know how to do
efficiently otherwise, though still not NP complete problems. Is
randomness really needed?
- Can we derandomize, can we get cryptography? If there are certain
kinds of "hard problems" then yes!
- We need to prove there are hard problems of a certain kind.
Some results are known - undecidable problems, hierarchy theorems.
But these are not enough. The kinds of results we need seem
far out of reach.
- The assigned reading for the next lecture, what we will talk
about next time - Turing machines as general-purpose computers,
uncomputable problems.