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# hw4 - exactly the template given in class Work modulo q =...

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University of Maryland CMSC652 — Complexity Theory Professor Jonathan Katz Homework 4 Due at the beginning of class on Nov. 16 I suggest to use L A T E Xwhen typing up your solutions. 1. Prove Claim 3 in the notes for lecture 12. Prove also that ZPP = RP ∩ co RP . 2. Arora-Barak, Exercise 7.10. 3. Arora-Barak, Exercise 8.1(d). 4. Arora-Barak, Exercise 8.4. 5. Consider the follow (true) TQBF statement φ : x 1 x 2 : ( x 1 ¯ x 2 ) x 1 x 2 ). (a) Write out the arithmetization Φ for φ , and prove that Y x 1 ∈{ 0 , 1 } R x 1 a x 2 ∈{ 0 , 1 } R x 1 R x 2 Φ( x 1 , x 2 ) = 1 mod 11 . (b) Explicitly write out the entire interactive proof for the statement above, following
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Unformatted text preview: exactly the template given in class. Work modulo q = 11, and assume that in the ﬁrst iteration the veriﬁer chooses “random value” 1, then “random value” 2, ..., etc. (This is only to make it easier for the TA to grade — in a real execution of the protocol, the veriﬁer would of course need to choose the random values at random, and we would have to take q larger than 11.) 1...
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