hw5 - CSci 5403, Spring 2010 Homework 5 due: April 1, 2010...

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CSci 5403, Spring 2010 Homework 5 due: April 1, 2010 1. Randomized reduction or proof. BP · NP to be the set of all languages having a randomized reduction to a language in NP . (A randomized reduction from L 1 to L T is a polynomial-time computable function f such that for any x L 1 , Pr[ f ( x ; r ) L T ] 2 3 and for any x 6∈ L 1 , Pr[ f ( x ; r ) L T ] 1 3 .) Prove that AM = BP · NP . 2. AM plification . Let AM c,d be the class of languages L with a constant-round Arthur- Merlin proof system ( P,V ) such that: x L Pr[ V accepts x] c . x 6∈ L Pr[ V accepts x] d . That is, 1 - c is the completeness error and d is the soundness error; the standard class AM defined in lecture is then AM 2 3 , 1 3 , and we also proved in lecture that AM 2 3 , 1 3 = AM 1 - 2 - n , 2 - n , that is, we can make the soundness and completness error exponentially close to 0. Unfortu- nately, no matter how many times we repeat this process we will never produce a soundness
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hw5 - CSci 5403, Spring 2010 Homework 5 due: April 1, 2010...

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