On Some Relations Between Approximation Problems and PCPs over the Real Numbers
In  it was recently shown that NPℝ ⊆ PCRℝ(poly, O(1)) i.e.the existence of transparent long proofs for NPℝ was established. The latter denotes the class of real number decision problems verifiable in polynomial time as introduced by Blum, Shub and Smale 
KeywordsPolynomial Time Approximation Problem Polynomial System Common Zero Polynomial Time Approximation Scheme
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