Final On-Campus FA05Sol

Final On-Campus FA05Sol - COT 5405 Analysis of Algorithms...

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Analysis of Algorithms Fall 2005 On-Campus Final Exam Page 1 of 11 COT 5405 Analysis of Algorithms Fall 2005 On-Campus Comprehensive Exam Name: __________________________________________ UFID: ____________ - ____________ E-mail: _________________________________________ Instructions: 1. Write neatly and legibly 2. While grading, not only your final answer but also your approach to the problem will be evaluated 3. You have to attempt all three problems (15 + 25 + 60 points). You have choices under the 3 rd problem. 5. Total time for the exam is 120 minutes 6. You are not allowed to use a calculator for this exam I have read carefully, and have understood the above instructions. On my honor, I have neither given nor received unauthorized aid on this examination. Signature: _____________________________________ Date: ____(MM) / ____(DD) / ___________(YYYY)
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Analysis of Algorithms Fall 2005 On-Campus Final Exam Page 2 of 11 Q1. (3 * 5 = 15 Points) Complete all three parts. You must write a very brief explanation for your answer for each question (without the justification, you will get very little credit): a) Consider the following problem: x 1 , x 2 , …, x n are Boolean variables that take either 0 (False) or 1 (True)value. You need to find out if there exists a set of assignments of Boolean values to these n variables such that the statement Φ (expressed in the following form: consisting of OR-ed clauses, and each clause consisting of literals) is evaluated to be true: = ( x 1 ¬ x 2 x 4 ) ( ¬ x n- 2 x 5 ¬ x 7 ) …. …. ( ¬ x 3 ¬ x n -5 ¬ x n ) The problem above is (tick all that applies): ± In P ± Not in P ± Not known to be in P ± In NP ± In NP-Hard ± In NP-Complete ± All of the above ± None of the above The catch is that the expression is not in CNF, but in DNF. Therefore it is not an NP-complete problem: it’s rather in P (and thus in NP).
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Final On-Campus FA05Sol - COT 5405 Analysis of Algorithms...

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