Probabilistic checking of proofs: A new characterization of NP

Sanjeev Arora*, Shmuel Safra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading 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.

Original languageEnglish
Pages (from-to)70-122
Number of pages53
JournalJournal of the ACM
Issue number1
StatePublished - Jan 1998


  • F.1.2 [Computation by Abstract Devices]: Modes of Computation
  • F.1.3 [Computation by Abstract Devices]: Complexity Classes
  • F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems


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