The PCP Theorem, proved in full by Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan and Mario Szegedy in 1998, building on earlier work including that of Laszlo Babai, Lance Fortnow and Carsten Lund, states that every decision problem in NP has a probabilistically checkable proof that a randomized verifier can check by reading only a constant number of bits, using only logarithmically many random bits, while still catching any incorrect proof with high probability. The theorem underlies the modern theory of hardness of approximation, and its original proof and Irit Dinur's later simplified 2005 proof using expander graphs each earned a Godel Prize.
Facts
StatementNP = PCP[O(log n), O(1)]: every problem in NP has a probabilistically checkable proof verifiable with logarithmic randomness and a constant number of queries. 1 Proof YearFull proof by Arora, Lund, Motwani, Sudan and Szegedy in 1998; precursor work by Arora and Safra in 1992. Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source PCP theorem, Wikipedia
Sources
1. PCP theorem, Wikipedia
Formal statement
NP = PCP[O(log n), O(1)]
History
a proof of the PCP theorem by Arora, Lund, Motwani, Sudan, and Szegedy in 1998
In Branch: Computational Complexity Theory, Lead sentence
In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision pr
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