### Probabilistic checking of proofs: a new characterization of NPProbabilistic checking of proofs: a new characterization of NP

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 Author Arora, Sanjeev ♦ Safra, Shmuel Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1998 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword NP-completeness ♦ Approximation algorithms ♦ Complexity hierarchies ♦ Computations on polynomials and finite fields ♦ Error-correcting codes ♦ Hardness of approximations ♦ Interactive computation ♦ Probabilistic computation ♦ Proof checking ♦ Reducibility and completeness ♦ Trade-offs/relations among complexity measures Abstract We give a new characterization of NP: the class NP contains exactly those languages $\textit{L}$ for which membership proofs (a proof that an input $\textit{x}$ is in $\textit{L})$ can be verified probabilistically in polynomial time using $\textit{logarithmic}$ number of random bits and by reading $\textit{sublogarithmic}$ number of bits from the proof.We discuss implications of this characterization; specifically, we show that approximating Clique and Independent Set, even in a very weak sense, is NP-hard. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1998-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 45 Issue Number 1 Page Count 53 Starting Page 70 Ending Page 122

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Source: ACM Digital Library