Abstract | ||
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There are significant obstacles to establishing an equivalence between the worst-case and average-case hardness of NP: Several results suggest that black-box worst-case to averagecase reductions are not likely to be used for reducing any worstcase problem outside coNP to a distributional NP problem. This paper overcomes the barrier. We present the first nonblack-box worst-case to average-case reduction from a problem outside coNP (unless Random 3SAT is easy for coNP algorithms) to a distributional NP problem. Specifically, we consider the minimum time-bounded Kolmogorov complexity problem (MINKT), and prove that there exists a zero-error randomized polynomial-time algorithm approximating the minimum time bounded Kolmogorov complexity k within an additive error ̅O(√ k) if its average-case version admits an errorless heuris tic polynomial-time algorithm. (The converse direction also holds under a plausible derandomization assumption.) We also show that, given a truth table of size 2
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup>
approximating the minimum circuit size within a factor of 2(
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-ε</sup>
jn is in BPP for some constant € > 0 if and only if its average-case version is easy. Based on our results, we propose a research program for excluding Heuristica, i.e., establishing an equivalence between the worst-case and average-case hardness of NP through the lens of MINKT or the Minimum Circuit Size Problem (MCSP). |
Year | DOI | Venue |
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2018 | 10.1109/FOCS.2018.00032 | 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) |
Keywords | DocType | Volume |
average case complexity,non-black-box reduction,time-bounded Kolmogorov complexity,minimum circuit size problem | Conference | 25 |
ISSN | ISBN | Citations |
1523-8288 | 978-1-5386-4231-3 | 1 |
PageRank | References | Authors |
0.35 | 35 | 1 |
Name | Order | Citations | PageRank |
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Shuichi Hirahara | 1 | 7 | 3.48 |