(poly(log log n), poly(log log n))-Restricted Verifiers are Unlikely to Exist for Languages in NP
نویسندگان
چکیده
The aim of this paper is to present a proof of the equivalence of the equalities N P = PCP(log log n; 1) and P = N P. The proof is based on producing long pseudo-random bit strings through random walks on expander graphs. This technique also implies that for any language in N P there exists a restricted veriier using log n + c, c is a constant, random bits. Furthermore, we prove that the equality of classes N P and PCP(poly(log log n); poly(log log n)) implies the inclusion of N P in DT IME ? n poly(log log n). Also, some technical details of the proof of N P = PCP(log n; 1) are used for showing that a certain class of (poly(log log n); poly(log log n)){restricted veriiers does not exist for languages in N P unless P = N P.
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