| Autor: |
Gu, Xiaoyang, Hitchcock, John M., Pavan, A. |
| Rok vydání: |
2010 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. 2. If there is a problem in coNP that cannot be solved by polynomial-size nondeterministic circuits, then every many-one complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. 3. If there exist a one-way permutation that is secure against subexponential-size circuits and there is a hard tally language in NP intersect coNP, then there is a Turing complete language for NP that is not many-one complete. Our first two results use worst-case hardness hypotheses whereas earlier work that showed similar results relied on average-case or almost-everywhere hardness assumptions. The use of average-case and worst-case hypotheses in the last result is unique as previous results obtaining the same consequence relied on almost-everywhere hardness results. |
| Databáze: |
arXiv |
| Externí odkaz: |
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