- 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 ( ).
- These results are sometimes also called PCP theorems because they can be viewed as probabilistically checkable proofs for NP with some additional structure.
- He was a winner of the G鰀el Prize in 2001 for his work on the PCP theorem and its applications to hardness of approximation.
- This result paved the way for the celebrated PCP theorem, which can be considered to be a " scaled-down " version of this theorem.
- The PCP theorem is the cornerstone of the theory of computational hardness of approximation, which investigates the inherent difficulty in designing efficient approximation algorithms for various optimization problems.
- The name of this theorem ( the " PCP theorem " ) probably comes either from "'" PCP " "'meaning " probabilistically checkable proof ", or from the notation mentioned above ( or both ).
- It's difficult to see pcp theorem in a sentence. 用pcp theorem造句挺難的
- In computational complexity theory, "'( SAT, ?-UNSAT ) "'is a language that is used in the proof of the PCP theorem, which relates the language NP to probabilistically checkable proof systems.
- The 2001 G鰀el Prize was awarded to Sanjeev Arora, Uriel Feige, Shafi Goldwasser, Carsten Lund, L醩zl?Lov醩z, Rajeev Motwani, Shmuel Safra, Madhu Sudan, and Mario Szegedy for work on the PCP theorem and its connection to hardness of approximation.
- After Arora et al . proved the PCP theorem a year later, it has now been shown that Johnson's 1974 approximation algorithms for Max SAT, Set Cover, Independent Set and Coloring all achieve the optimal approximation ratio, assuming P ! = NP.
- Building upon previous work on the PCP theorem, Johan H錽tad showed that, assuming P ` " NP, no polynomial-time algorithm for MAX 3SAT can achieve a performance ratio exceeding 7 / 8, even when restricted to satisfiable instances of the problem in which each clause contains exactly three literals.
- The PCP theorem says that for some universal constant " K ", for every " n ", any mathematical proof of length " n " can be rewritten as a different proof of length poly ( " n " ) that is formally verifiable with 99 % accuracy by a randomized algorithm that inspects only " K " letters of that proof.
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