# exam1 - CSE860 Exam Due: 5 pm March 19. PART I. Solve the...

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CSE860 Exam Due: 5 pm March 19. PART I. Solve the following three problems. 1. Suppose that (i) A and B are problems in P, (ii) C and D are in NP, (iii) E is NP-complete. (iv) F is co-NP. For each of the following questions, answer either "false" (i.e., not necessarily true), "true if NP = P", always "true" (i.e., regardless of the fact whether P = NP). For a problem X, X C refers to the complement problem of X. Explain your answer in one sentence. a) A is polynomial time reducible to A C . b) D is polynomial time Turing reducible to D C . c) F is polynomial reducible to E. d) E is polynomial time Turing reducible to A. e) E is polynomial time reducible to E C f) A is in co-NP. g) if 3SAT is polynomial time reducible to C, C is NP-complete. 2. Solve 6.9. 3. Solve 6.3

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PART II. Select 4 and solve them. 4. Solve 5.2. 5. Solve 7.36 6. Consider the set cover problem. Instance : Set S and a collection C of subsets of S, and integer k Question : Does there exist a subset D of C such that D covers S and |D| <= k? We say D covers S if for any element x in S, there is A in D such that x
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## This note was uploaded on 07/25/2008 for the course CSE 860 taught by Professor Chung during the Spring '04 term at Michigan State University.

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exam1 - CSE860 Exam Due: 5 pm March 19. PART I. Solve the...

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