Almost Transparent Short Proofs for NPℝ
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(logn), polylog(n)), i.e., each decision problem in NPℝ is accepted by a verifier that generates O(logn) 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)).
KeywordsPolynomial System Univariate Polynomial Probabilistic Check Proof Logarithmic Number Real Number Model
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