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2004
Springer

Properties of NP-Complete Sets

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Properties of NP-Complete Sets
We study several properties of sets that are complete for NP. We prove that if L is an NP-complete set and S ⊇ L is a p-selective sparse set, then L − S is ≤p m-hard for NP. We demonstrate existence of a sparse set S ∈ DTIME(22n ) such that for every L ∈ NP − P, L − S is not ≤p m-hard for NP. Moreover, we prove for every L ∈ NP − P, that there exists a sparse S ∈ EXP such that L − S is not ≤p m-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 resolve longstanding 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 ...
Christian Glaßer, Aduri Pavan, Alan L. Selma
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where COCO
Authors Christian Glaßer, Aduri Pavan, Alan L. Selman, Samik Sengupta
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