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

  • Authors:
  • R. Impagliazzo

  • Affiliations:
  • Dept. of Comput. Sci., Toronto Univ., Ont., Canada

  • Venue:
  • SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
  • Year:
  • 1990

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Abstract

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.