Unformatted text preview: leave it to Arthur to verify in polynomial time). Since Arthur runs in polynomial time, by the CookLevin reduction there is a 3SAT formula φ x r with free variables a such that φ x r a ) iF Arthur accepts Merlin’s argument a , and L T = x r ) : ∃ aφ x r a ) } . Let f x ; r ) = φ x r . If x ∈ L , then with probability at least 2 / 3, Merlin can convince Arthur to accept, meaning x r ) ∈ L T and φ x r ∈ 3SAT . In other words, if x ∈ L then Pr r [ f x ; r ) ∈ 3SAT ] ≥ 2 / 3. If x / ∈ L , then with probability at most 1 / 3, Merlin can convince Arthur to accept, meaning x r ) ∈ L T . In other words, if x / ∈ L then Pr r [ f x ; r ) ∈ 3SAT ] ≤ 1 / 3....
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 Spring '08
 Sturtivant,C
 Logic, 3SAT

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