1. Define what is P, what is NP, what is NP-hard, and what is NP-complete; no need to give a detailed definition of reduction. Which of these three classes contain the problem of adding all numbers in a given array? the 3-coloring problem?
2-6. Reduce the satisfiability problem for the formula (~x1 \/ x2) & (x1 \/ ~x2) & (~x1 \/ x2 \/ x3) to:
7-9. A straightforward algorithm takes time O(n) to compute the sum of all the elements in an array of size n.
10. If a probabilistic algorithm produces a result with the probability of error 1/2, how many times do we need to repeat it to reduce the probability of error to 1%?
11. Find what is Π4PΣ2P.
12. Which class of the polynomial hierarchy corresponds to winning in two steps -- i.e., after you make your move, whatever move the opponent makes, you win.