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Prove MAX-3SAT not approximable within 7/8 unless P=NP
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Prove MAX-3SAT not approximable
within 7/8 unless P=NP
Analyze the prove max-3sat not approximable within 7/8 unless p=np.
Examples
Example 1
Input:
"test_input_1"
Output:
"output_1"
Example 2
Input:
"test_input_2"
Output:
"output_2"
Hints
Hint 1
Recall the PCP theorem and its implications on the hardness of approximation for NP-hard problems.
Hint 2
Consider how the gap version of Max-3SAT can be constructed to leverage the PCP theorem's guarantees.
Hint 3
Analyze the specific gap introduced by the PCP theorem (e.g., completeness/soundness parameters) to derive the 7/8 inapproximability threshold.
Prove MAX-3SAT not approximable within 7/8 unless P=NP
Analyze the prove max-3sat not approximable within 7/8 unless p=np.