Learning secrets interactively. Dynamic modeling in inductive inference

  • Authors:

  • John Case;Timo KöTzing

  • Affiliations:

  • Department of Computer and Information Sciences, University of Delaware, Newark, DE 19716, USA;Department 1: Algorithms and Complexity, Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2012

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Abstract

Introduced is a new inductive inference paradigm, dynamic modeling. Within this learning paradigm, for example, function h learns function g iff, in the i-th iteration, h and g both produce output, h gets the sequence of all outputs from g in prior iterations as input, g gets all the outputs from h in prior iterations as input, and, from some iteration on, the sequence of h@?s outputs will be programs for the output sequence of g. Dynamic modeling provides an idealization of, for example, a social interaction in which h seeks to discover program models of g@?s behavior it sees in interacting with g, and h openly discloses to g its sequence of candidate program models to see what g says back. Sample results: every g can be so learned by some h; there are g that can only be learned by an h if g can also learn that h back; there are extremely secretive h which cannot be learned back by any g they learn, but which, nonetheless, succeed in learning infinitely many g; quadratic time learnability is strictly more powerful than linear time learnability. This latter result, as well as others, follows immediately from general correspondence theorems obtained from a unified approach to the paradigms within inductive inference. Many proofs, some sophisticated, employ machine self-reference, a.k.a., recursion theorems.