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53+Slides--The+Cook-Levin+Theorem

# 53+Slides--The+Cook-Levin+Theorem - CS103 HO#53 Slides-The...

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CS103 HO#53 Slides--The Cook-Levin Theorem 5/25/11 1 Polynomial Time Mapping Reductions A B Theorem 7.31 : If A P B and B P, then A P. Suppose B has a polynomial time solution. Then so does A. P P Map the problem to B Problem for A Decider for B Decider for A Problem for b Decision for A B NP-Completeness P NP NPC P P P P Theorem 7.31 : If A P B and B P, then A P. Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. B NP-Completeness P NP NPC P P P P Theorem 7.31 : If A P B and B P, then A P. Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. What if B is in P? B NP-Completeness P NP NPC P P P P Theorem 7.31 : If A P B and B P, then A P. Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. What if B is in P? B NP-Completeness P NP NPC P P P P Theorem 7.31 : If A P B and B P, then A P. Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. What if B is in P? B NP-Completeness P NP NPC P P P P Theorem 7.31 : If A P B and B P, then A P. Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. What if B is in P?

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CS103 HO#53 Slides--The Cook-Levin Theorem 5/25/11 2 Adi Shamir, Ronald Rivest, and Len Adleman publish RSA at MIT in 1977. The Inventors of RSA Cryptography B NP-Completeness P NP NPC Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. Theorem 7.36 : If B is NP-complete and B P C for C NP, then C NPC . P P P P Theorem 7.31 : If A P B and B P, then A P. C P B NP-Completeness P NP NPC Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. Theorem 7.36 : If B is NP-complete and B P C for C NP, then C NPC . Theorem 7.31 : If A P B and B P, then A P. C P B NP-Completeness P NP NPC Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. How do we start the process of finding members of NPC? Theorem 7.36 : If B is NP-complete and B P C for C NP, then C NPC.
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