We present results concerning the learning of Monotone DNF (MDNF) from Incomplete Membership Queries and Equivalence Queries. Our main result is a new algorithm that allows efficient learning of MDNF using Equivalence Queries and Incomplete Membership Queries with probability of p = 1− 1/poly(n, t) of failing. Our algorithm is expected to make (formula presented) queries, when learning a MDNF formula with t terms over n variables. Note that this is polynomial for any failure probability p = 1 − 1/poly(n, t). The algorithm’s running time is also polynomial in t, n, and 1/(1 − p). In a sense this is the best possible, as learning with p = 1−1/ω(poly(n, t)) would imply learning MDNF, and thus also DNF, from equivalence queries alone.
CITATION STYLE
Bshouty, N. H., & Eiron, N. (2001). Learning monotone DNF from a teacher that almost: Does not answer membership queries. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2111, pp. 546–557). Springer Verlag. https://doi.org/10.1007/3-540-44581-1_36
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