Aizenstein, Howard; Blum, Avrim; Khardon, Roni; Kushilevitz, Eyal; Pitt, Leonard On learning read-\(k\)-satisfy-\(j\) DNF. (English) Zbl 0907.68145 SIAM J. Comput. 27, No. 6, 1515-1530 (1998). Summary: We study the learnability of read-\(k\)-satisfy-\(j\) (RkSj) DNF formulas. These are boolean formulas in disjunctive normal form (DNF), in which the maximum number of occurrences of a variable is bounded by \(k\), and the number of terms satisfied by any assignment is at most \(j\). After motivating the investigation of this class of DNF formulas, we present an algorithm that for any unknown RkSj DNF formula to be learned, with high probability finds a logically equivalent DNF formula using the well-studied protocol of equivalence and membership queries. The algorithm runs in polynomial time for \(k\cdot j=O({\log n\over\log\log n})\), where \(n\) is the number of input variables. Cited in 4 Documents MSC: 68T05 Learning and adaptive systems in artificial intelligence 68Q25 Analysis of algorithms and problem complexity Keywords:DNF; learning; computational learning theory; decision trees PDFBibTeX XMLCite \textit{H. Aizenstein} et al., SIAM J. Comput. 27, No. 6, 1515--1530 (1998; Zbl 0907.68145) Full Text: DOI