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final - University of Maryland CMSC652 Complexity Theory...

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University of Maryland CMSC652 — Complexity Theory Professor Jonathan Katz Final Exam Instructions: The completed exam must be turned in by 3:30 on Dec. 19. You may hand it to me in person or (1) email me a pdf; (2) slide it under my door; (3) put it in my CS mailbox on the first floor. In the latter two cases, you should follow up with an email to make sure I received it. You may use any results from class (plus course notes) or the Arora-Barak textbook, but no other sources. Show your work for partial credit. 1. (2 points) What was your favorite thing you learned this semester? 2. (14 points) Consider the promise problem Π Y = { ( ϕ, ϕ 0 ) : ϕ SAT , ϕ 0 SAT } Π N = { ( ϕ, ϕ 0 ) : ϕ SAT , ϕ 0 SAT } . Show that if this problem is in promise- P , then P = NP . 3. (30 points) Language L is in BP · NP if it has a “randomized Karp reduction” to 3- SAT ; namely, if there is a probabilistic poly-time Turing machine M such that x L Pr[ M ( x ) 3- SAT ] 3 / 4 x 6∈ L Pr[ M ( x ) 3- SAT ] 1 / 4 .
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  • Fall '08
  • staff
  • Computational complexity theory, Professor Jonathan Katz, satisfying assignments, promise problem, randomized Karp reduction, probabilistic poly-time Turing

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