Question text is in black, my answers in blue.
For Exercise 2.2, where we need to identify which of these NP problems are in P, what exactly are we supposed to prove? Your hints seem to give everything away.
This is certainly not a difficult problem given the hints, but you still have to explain why the proven and assumed facts tell whether each language is in P or not.
For the ones in P, do we just need to give a poly-time algorithm?
Yes, exactly, and now you don't have to worry about the specifics of Turing machines but just describe an algorithm that is poly-time in any reasonable model.
In Exercise 2.16, we are asked to prove that MAX-CUT is NP-complete. I did this problem in 611, where we reduced from NotAllEqual-3SAT. Am I allowed to use this? And if I am, must I give both the reduction from NAE-3SAT and the proof that NAE-3SAT is itself NP-complete?
Yes, if you do it that way you must at least sketch both reductions, and credit your sources. By the way, the online draft of [AB] gives the hint that you should reduce from IND-SET, and the diagram on page 55 of the printed [AB] indicates that Exercise 2.16 is to be solved by reduction from VERTEX-COVER. But any valid argument will do. Sipser's book does it from NAE-3SAT in an exercise.
Last modified 14 February 2010