Crytographic limitations on learning Boolean formulae and finite automata

  title={Crytographic limitations on learning Boolean formulae and finite automata},
  author={M. Kearns and L. Valiant},
  booktitle={STOC '89},
In this paper we consider the problem of learning from examples classes of functions when there are no restrictions on the allowed hypotheses other than that they are polynomial time evaluatable. We prove that for Boolean formulae, finite automata, and constant depth threshold circuits (simplified neural nets), this problem is computationally as difficult as the quadratic residue problem, inverting the RSA function and factoring Blum integers (composite number p q where p and q are both primes… Expand
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