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    P(APP) = P(prBPP)

    Moser, Philippe (2002) P(APP) = P(prBPP). Technical Report. Electronic Colloquium on Computational Complexity.

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    We show that for deterministic polynomial time computations, oracle access to APP, the class of real functions approximable by probabilistic Turing machines, is the same as having oracle access to promise-BPP. First, we construct a mapping that maps every function in APP to a promise problem in prBPP, and that preserves completeness, i.e. maps complete functions to complete promise problems. Next, we construct a mapping from prBPP into APP, that maps every promise problem to a function in APP, and which preserves completeness. Then, we prove that PAPP=PprBPP. Finally, we use our results to simplify proofs of important results on APP, such as the APP-completeness of the function fCAPP, which approximates the acceptance probability of a Boolean circuit, the error probability reduction Theorem for APP functions, and the conditional derandomization result APP=AP iff prBPP is easy.

    Item Type: Monograph (Technical Report)
    Keywords: computationnal complexity; Randomness;
    Academic Unit: Faculty of Science and Engineering > Computer Science
    Item ID: 10308
    Identification Number: Revision #1 to TR01-068
    Depositing User: Philippe Moser
    Date Deposited: 11 Dec 2018 15:58
    Publisher: Electronic Colloquium on Computational Complexity
      Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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