CS 5315, Test 2, Wednesday, April 30, 2014


(Please do not forget to put your name on all extra sheets of paper)

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 dot product (a, b) = a1 * b1 + ... + an * bn of two vectors a = (a1, ..., an) and b = (b1, ..., bn) of size n? the main problem of interval computations?

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 dot product of two vectors of size n.

10. If a probabilistic algorithm produces a result with the probability of error 1/4, how many times do we need to repeat it to reduce the probability of error to 0.1%?

11. Find what is Π2PΣ4P.

12. Which class of the polynomial hierarchy corresponds to winning in three moves?

13. What is the Kolmogorov complexity of a sequence 100100 ... 100 (repeated 2,014 times)?