Abstract
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)).
Partially supported by DFG project ME 1424/7-1.
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Meer, K. (2011). Almost Transparent Short Proofs for NPℝ . In: Owe, O., Steffen, M., Telle, J.A. (eds) Fundamentals of Computation Theory. FCT 2011. Lecture Notes in Computer Science, vol 6914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22953-4_4
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DOI: https://doi.org/10.1007/978-3-642-22953-4_4
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