Constructing Hard Functions from Learning Algorithms

@article{Klivans2013ConstructingHF,
  title={Constructing Hard Functions from Learning Algorithms},
  author={Adam R. Klivans and Pravesh Kothari and Igor Carboni Oliveira},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2013},
  volume={20},
  pages={129}
}
Fortnow and Klivans proved the following relationship between efficient learning algorithms and circuit lower bounds: if a class C ⊆ P/poly of Boolean circuits is exactly learnable with membership and equivalence queries in polynomial-time, then EXP * C (the class EXP was subsequently improved to EXP by Hitchcock and Harkins). In this paper, we improve on these results and show • If C is exactly learnable with membership and equivalence queries in polynomial-time, then DTIME(n) 6⊆ C. We obtain… CONTINUE READING

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