Learning a circuit by injecting values

d Abstract] Dana Angluin James Aspnes Jiang Chen Yinghua Wu 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 learnable 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 bounded depth and unbounded fan-in over AND, OR, and threshold gates, even when the target circuit i...

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: Dana Angluin, James Aspnes, Jiang Chen, Yinghua Wu
• Keywords: Algorithms, Arbitrary Circuits, Boolean Circuits, STOC 2006, Unbounded Depth