homework3 - CSE 200 Computability and Complexity Homework 3...

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CSE 200 Computability and Complexity Homework 3 The class NP and beyond, Completeness, and Reductions Polynomial-time Hierarchy Space Complexity Due May 26 May 11, 2010 Give proofs for each problem. Proofs can be high-level, but be precise. You may use without giving a proof any result proved in class or in the textbook. In particular, to prove NP-completeness, it suFces to give a reduction from any of the NP-complete problems from the text or from class. However, you must show your reduction is valid, by showing the equivalence of the constructed instance and the original. NP and co - NP Consider the problem Greater Maximum Independent Set: Given G 1 and G 2 , is the maximum independent set for G 1 strictly larger than that for G 2 ? Show that this problem is in NP if and only if it is in Co - NP if and only if NP = co - NP . NP-Completeness We say that NP complete problems are the “hardest” in NP , but intuitively that means they are the “least likely to be easy” not that they have the greatest worst-case complexity. To illustrate
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homework3 - CSE 200 Computability and Complexity Homework 3...

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