08 - The Cook-Levin Theorem

# 08 - The Cook-Levin Theorem - 26 3/14/08 - The Cook-Levin...

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3/14/08 - The Cook-Levin Theorem Today: The Cook-Levin Theorem (3SAT is NP-complete) Step 1: 4SAT p 3SAT p ? 2SAT (no reduction to 2SAT) <- p Given 4SAT instance (x 1 x ̅ 2 x3 x4) (x2 x ̅ 4 x5 x 6 ) ϕ (x 1 x ̅ 2 z 1 ) (z ̅ 1 x 3 x 4 ) (x 2 x ̅ 4 z 2 ) (z ̅ 2 x 5 x 6 ) ϕ ̂ x 3 = x 5 = 1 z 1 = z 2 = 1 ϕ satisfable <=> ϕ ̂ satisfable Turing Machines: A Turing machine is a program given by: fnite alphabet oF symbols Σ (special _ char.) fnite set oF states K. (special “yes”, “no” states) infnite tape containing seq. oF symbols. (fnitely many _) state transition table δ δ (i, σ ) tells what to do in state i, reading σ . (1) a symbol to write at current position (2) a direction (L or R) to move next on the tape (3) a state to go into next s = start 26-1 26

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state symbol What now? s 0 0, , s //starting state, go til _ s 1 1, , s s _ _, , t t 1 1, , t //go til 0
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## This note was uploaded on 10/02/2008 for the course CS 482 taught by Professor Kleinberg during the Spring '08 term at Cornell.

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08 - The Cook-Levin Theorem - 26 3/14/08 - The Cook-Levin...

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