No better ways to generate hard NP instances than picking uniformly at random

Distributed NP (DNP) problems are ones supplied with probability distributions of instances. It is shown that every DNP problem complete for P-time computable distributions is also complete for all distributions that can be sampled. This result makes the concept of average-case NP completeness robus...

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Bibliographic Details
Published inFoundations of Computer Science, 31st Symposium pp. 812 - 821 vol.2
Main Authors Impagliazzo, R., Levin, Leonid A
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1990
Subjects
Computer science
Cryptography
Distributed computing
Extrapolation
Matrix decomposition
NP-complete problem
Polynomials
Probability distribution
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ISBN081862082X
9780818620829
DOI10.1109/FSCS.1990.89604

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Summary:Distributed NP (DNP) problems are ones supplied with probability distributions of instances. It is shown that every DNP problem complete for P-time computable distributions is also complete for all distributions that can be sampled. This result makes the concept of average-case NP completeness robust and the question of the average-case complexity of complete DNP problems a natural alternative to P=?NP. Similar techniques yield a connection between cryptography and learning theory.
ISBN:081862082X
9780818620829
DOI:10.1109/FSCS.1990.89604