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Authors: Bshouty, Nader H.
Cleve, Richard
Tamon, Christino
Kannan, Sampath
Keywords: Computer Science
Issue Date: 1-Apr-1994
Abstract: We show that the class of all circuits is exactly learnable in (randomized) expected polynomial-time using subset and superset queries. Subset and superset queries are a generalization of equivalence queries, where an instance of a negative counterexample is requested (for subset queries) or a positive counterexample is requested (for superset queries). Our result is a consequence of the following result which we consider to be of independent interest: the class of all circuits is exactly learnable in (randomized) expected polynomial-time with equivalence queries and the aid of an NP-oracle. This improves the previous result of Gavald\o'a\(ga' [G93] where a $SIGMA~pile {p above 3 }$-oracle and equivalence queries are required in place of the NP-oracle and equvalence queries, and the learning algorithm is deterministic. The hypothesis class for both of the above learning algorithms is the class of circuits of slightly larger (polynomially related) size. Also, the algorithms can be adapted to learn the class of DNF formulas with hypothesis class consisting of depth-3 $andsign - orsign - andsign$ formulas (by the work of Angluin [A90], this is optimal in the sense that the hypothesis class cannot be reduced to depth-2 DNF formulas). We also found deterministic learning algorithms that use \fImembership\fR queries and the NP-oracle for learning monotone boolean functions and the class 0(log $n$)-DNF $cap$ 0(log $n$)-CNF. The running time of these algorithms are polynomial in $n$, DNF size and CNF size of the target formula. Finally with an NP-oracle and membership queries, there is a randomized polynomial-time algorithm that learns any class that is learnable from membership queries with unlimited computational power.
Appears in Collections:Bshouty, Nader
Cleve, Richard

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