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- Any NP-complete problem by the PCP theorem.
- In 2005 Irit Dinur discovered a different proof of the PCP theorem, using expander graphs.
- The PCP theorem is the culmination of a long line of work on interactive proofs and probabilistically checkable proofs.
- Furthermore, the PCP theorem asserts that the number of proof accesses can be brought all the way down to a constant.
- Expander graphs have found extensive applications in computer science, in designing algorithms, L ( ) and the PCP theorem ( ).