Communications of the ACM
Logic testing and design for testability
Logic testing and design for testability
Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Learning read-once formulas with queries
Journal of the ACM (JACM)
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
Cryptographic hardness of distribution-specific learning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
When won't membership queries help?
Selected papers of the 23rd annual ACM symposium on Theory of computing
Exact learning Boolean functions via the monotone theory
Information and Computation
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
Identification of gene regulatory networks by strategic gene disruptions and gene overexpressions
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Optimally Learning Social Networks with Activations and Suppressions
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Learning a circuit by injecting values
Journal of Computer and System Sciences
Learning large-alphabet and analog circuits with value injection queries
COLT'07 Proceedings of the 20th annual conference on Learning theory
Completing networks using observed data
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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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 is known to contain at most one threshold gate and that threshold gate has threshold 2. We also consider the effect of adding an oracle for behavioral equivalence. In this case there are polynomial-time algorithms to learn arbitrary circuits of constant fan-in and unbounded depth and to learn Boolean circuits with arbitrary fan-in and unbounded depth over AND, OR, and NOT gates. A corollary is that these two classes are PAC-learnable if experiments are available.