Hardness vs randomness
نویسندگان
چکیده
منابع مشابه
Hardness vs Randomness
We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE, ...) using an arbitrary function that is hard for C. This construction reveals an equivalence between the problem of proving lower b...
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We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f : {0, 1} → {0, 1} that is mildly hard on average, i.e. every circuit of size 2 fails to compute f on at least a 1/poly(l) fraction of inputs, we can build a PRG : {0, 1} n) → {0, 1} computable in ATIME (O(1), log n) = alternating time O(lo...
متن کاملLimitations of Hardness vs. Randomness under Uniform Reductions
We consider (uniform) reductions from computing a function f to the task of distinguishing the output of some pseudorandom generator G from uniform. Impagliazzo and Wigderson [IW] and Trevisan and Vadhan [TV] exhibited such reductions for every function f in PSPACE. Moreover, their reductions are “black box,” showing how to use any distinguisher T , given as oracle, in order to compute f (regar...
متن کاملUniform hardness vs. randomness tradeoffs for Arthur-Merlin games
Impagliazzo and Wigderson proved a uniform hardness vs. randomness ”gap result” for BPP. We show an analogous result for AM: Either ArthurMerlin protocols are very strong and everything in E = DTIME(2) can be proved to a sub-exponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm in the uniform average-case se...
متن کاملWorst-Case Hardness Suffices for Derandomization: A New Method for Hardness-Randomness Trade-Offs
Up to now, the known derandomization methods for BPP have been derived assuming the existence of an ExP function that has a "hard" average-case circuit complexity. In this paper we instead present the first construction of a de-randomization method for BOP that relies on the existence of an EXP function that is hard only in the worst-case. The construction is based on a new method that departs ...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1994
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(05)80043-1