## Efficient Checking of Polynomials and Proofs and the Hardness of Approximation Problems (1992)

Citations: | 68 - 9 self |

### BibTeX

@MISC{Sudan92efficientchecking,

author = {Madhu Sudan},

title = {Efficient Checking of Polynomials and Proofs and the Hardness of Approximation Problems},

year = {1992}

}

### OpenURL

### Abstract

The definition of the class NP [Coo71, Lev73] highlights the problem of verification of proofs as one of central interest to theoretical computer science. Recent efforts have shown that the efficiency of the verification can be greatly improved by allowing the verifier access to random bits and accepting probabilistic guarantees from the verifier [BFL91, BFLS91, FGL + 91, AS92]. We improve upon the efficiency of the proof systems developed above and obtain proofs which can be verified probabilistically by examining only a constant number of (randomly chosen) bits of the proof. The efficiently verifiable proofs constructed here rely on the structural properties of low-degree polynomials. We explore the properties of these functions by examining some simple and basic questi...