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 computing the sum of two matrices? the 4-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(N2) to compute the sum of two matrices of size N X 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 0.1%?
11. Find what is Σ4PΠ2P.
12. Which class of the polynomial hierarchy corresponds to finding the best alternative -- i.e., an alternative x for which objective function f(x) attains the largest possible value?
13. What is the Kolmogorov complexity of a sequence 010010 ... 010 (repeated 2,013 times)?