Abstract
We design a probabilistic test verifying whether a given table of real function values corresponds to a trigonometric polynomial f : F k ↦ℝ of certain (low) degree. Here, F is a finite field. The problem is studied in the framework of real number complexity as introduced by Blum, Shub, and Smale. Our main result is at least of a twofold interest. First, it provides one of two major lacking ingredients for proving a real PCP theorem along the lines of the proof of the original PCP theorem in the Turing model. Secondly, beside the PCP framework it adds to the still small list of properties that can be tested in the BSS model over ℝ.
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Baartse, M., Meer, K. (2014). Testing Low Degree Trigonometric Polynomials. In: Hirsch, E.A., Kuznetsov, S.O., Pin, JÉ., Vereshchagin, N.K. (eds) Computer Science - Theory and Applications. CSR 2014. Lecture Notes in Computer Science, vol 8476. Springer, Cham. https://doi.org/10.1007/978-3-319-06686-8_7
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DOI: https://doi.org/10.1007/978-3-319-06686-8_7
Publisher Name: Springer, Cham
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