PCP theorem
A milestone theorem in complexity theory asserting that NP = PCP[O(log n), O(1)]. It states that a proof for any NP problem can be encoded in a format verifiable with high probability by reading only a constant number of randomly selected bits, laying the foundation for the theory of inapproximability.
Timeline (last 90 days)
The PCP theorem was proved in the 1990s.
The PCP theorem shows that NP = PCP[O(log n), O(1)], that is, the verifier uses O(log n) random bits and reads O(1) proof bits.
The PCP theorem laid the foundation for the theory of hardness of approximation, showing that even distinguishing between 100% satisfiable and 99% satisfiable can be equally hard.
The Unique Games Conjecture is a strengthened form of the PCP theorem, involving a special type of label cover instance.
All Facts (4)
The PCP theorem was proved in the 1990s.
50%UnverifiedThe PCP theorem shows that NP = PCP[O(log n), O(1)], that is, the verifier uses O(log n) random bits and reads O(1) proof bits.
50%UnverifiedThe PCP theorem laid the foundation for the theory of hardness of approximation, showing that even distinguishing between 100% satisfiable and 99% satisfiable can be equally hard.
50%UnverifiedThe Unique Games Conjecture is a strengthened form of the PCP theorem, involving a special type of label cover instance.
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