Summary: Learning a Circuit by Injecting Values
Dana Angluin a
James Aspnes a,1
Jiang Chen b
Yinghua Wu a,3
aDepartment of Computer Science, Yale University.
bCenter for Computational Learning Systems, Columbia University.
Preprint submitted to Elsevier 7 March 2008
We propose a new model for exact learning of acyclic circuits using experiments
in which chosen values may be assigned to an arbitrary subset of wires internal to
the circuit, but only the value of the circuit's single output wire may be observed.
We give polynomial time algorithms to learn (1) arbitrary circuits with logarithmic
depth and constant fan-in and (2) Boolean circuits of constant depth and unbounded
fan-in over AND, OR, and NOT gates. Thus, both AC0 and NC1 circuits are learn-
able in polynomial time in this model. Negative results show that some restrictions
on depth, fan-in and gate types are necessary: exponentially many experiments are
required to learn AND/OR circuits of unbounded depth and fan-in; it is NP-hard
to learn AND/OR circuits of unbounded depth and fan-in 2; and it is NP-hard to
learn circuits of constant depth and unbounded fan-in over AND, OR, and threshold