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- W4300432017 abstract "We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the discrete Fourier transforms of linear functions with seed-length that is nearly logarithmic (up to polyloglog factors) in the input size and the desired error parameter. Our result gives a single pseudorandom generator that fools several important classes of tests computable in logspace that have been considered in the literature, including halfspaces (over general domains), modular tests and combinatorial shapes. For all these classes, our generator is the first that achieves near logarithmic seed-length in both the input length and the error parameter. Getting such a seed-length is a natural challenge in its own right, which needs to be overcome in order to derandomize RL - a central question in complexity theory. Our construction combines ideas from a large body of prior work, ranging from a classical construction of [NN93] to the recent gradually increasing independence paradigm of [KMN11, CRSW13, GMRTV12], while also introducing some novel analytic machinery which might find other applications." @default.
- W4300432017 created "2022-10-03" @default.
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- W4300432017 date "2015-06-14" @default.
- W4300432017 modified "2023-09-27" @default.
- W4300432017 title "Pseudorandomness via the discrete Fourier transform" @default.
- W4300432017 doi "https://doi.org/10.48550/arxiv.1506.04350" @default.
- W4300432017 hasPublicationYear "2015" @default.
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