Summary: Restriction Access
We introduce a notion of non-black-box access to computational devices (such as circuits,
formulas, decision trees, and so forth) that we call restriction access. Restrictions are partial
assignments to input variables. Each restriction simplifies the device, and yields a new device for
the restricted function on the unassigned variables. On one extreme, full restrictions (assigning
all variables) correspond to evaluating the device on a complete input, yielding the result of
the computation on that input, which is the same as standard black-box access. On the other
extreme, empty restrictions (assigning no variables) yield a full description of the original device.
We explore the grey-scale of possibilities in the middle.
Focusing on learning theory, we show that restriction access provides a setting in which one
can obtain positive results for problems that have resisted attack in the black-box access model.
We introduce a PAC-learning version of restriction access, and show that one can efficiently
learn both decision trees and DNF formulas in this model. These two classes are not known to
be learnable in the PAC model with black-box access.
Our DNF learning algorithm is obtained by a reduction to a general learning problem we call