Dynamic modeling in inductive inference

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; quadratictime learnablity is strictly more powerful than lintime learnablity. This latter result, as well as others, follow 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. © 2008 Springer-Verlag Berlin Heidelberg.