Self-testing polynomial functions efficiently and over rational domains
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Complexity and real computation
Complexity and real computation
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Transparent Long Proofs: A First PCP Theorem for NPR
Foundations of Computational Mathematics
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Some Relations between Approximation Problems and PCPs over the Real Numbers
Theory of Computing Systems
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Probabilistic checking of proofs; a new characterization of NP
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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We study probabilistically checkable proofs (PCPs) in the real number model of computation as introduced by Blum, Shub, and Smale. Our main result is NPR = PCPR(O(log n), polylog(n)), i.e., each decision problem in NPR is accepted by a verifier that generates O(log n) many random bits and reads polylog(n) many proof components. This is the first non-trivial characterization of NPR by real PCPR-classes. As a byproduct this result implies as well a characterization of real nondeterministic exponential time via NEXPR = PCPR(poly(n), poly(n)).