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• W2158543896 abstract "We study several properties of sets that are complete for NP. We prove that if L is an NP-complete set and S /spl nsupe/ L is a p-selective sparse set, then L -S is /spl les//sub m//sup p/-hard for NP. We demonstrate existence of a sparse set S /spl isin/ DTIME(2/sup 2n/) such that for every L /spl isin/ NP - P, L - S is not /spl les//sub m//sup p/-hard for NP. Moreover, we prove for every L /spl isin/ NP - P, that there exists a sparse S /spl isin/ EXP such that L - S is not /spl les//sub m//sup p/-hard for NP. Hence, removing sparse information in P from a complete set leaves the set complete, while removing sparse information in EXP from a complete set may destroy its completeness. Previously, these properties were known only for exponential time complexity classes. We use hypotheses about pseudorandom generators and secure one-way permutations to derive consequences for long-standing open questions about whether NP-complete sets are immune. For example, assuming that pseudorandom generators and secure one-way permutations exist, it follows easily that NP-complete sets are not p-immune. Assuming only that secure one-way permutations exist, we prove that no NP-complete set is DTIME(2/sup ne/)-immune. Also, using these hypotheses we show that no NP-complete set is quasipolynomial-close to P. We introduce a strong but reasonable hypothesis and infer from it that disjoint Turing-complete sets for NP are not closed under union. Our hypothesis asserts existence of a UP-machine M that accepts 0* such that for some 0 < /spl epsi/ < 1, no 2/sup ne/ time-bounded machine can correctly compute infinitely many accepting computations of M, We show that if UP /spl cap/ coUP contains DTIME(2/sup ne/)-bi-immune sets, then this hypothesis is true." @default.
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• W2158543896 date "2004-06-21" @default.
• W2158543896 modified "2023-09-26" @default.
• W2158543896 title "Properties of NP-complete sets" @default.
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• W2158543896 doi "https://doi.org/10.1109/ccc.2004.27" @default.
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