Read-Twice DNF Formulas Are Properly Learnable
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It is shown that read-twice DNF formulas-Boolean formulas in disjunctive normal form in which each variable appears at most twice-are exactly and properly learnable in polynomial time.Abstract:
We show that read-twice DNF formulas-Boolean formulas in disjunctive normal form in which each variable appears at most twice-are exactly and properly learnable in polynomial time. Our algorithm uses membership queries and proper equivalence queries and is based on a simple, new characterization of minimal read-twice DNF formulas. The algorithm improves on earlier results of Hancock and Aizenstein and Pitt which showed that read-twice DNF formulas are learnable using more powerful equivalence queries, i.e., where the hypotheses could be arbitrary DNF formulas. We also improve on the time-complexity of these earlier algorithms. Other results which may be of independent interest outside of learning follow directly from this paper. Specifically, we show that read-twice DNF formulas can be tested for equivalence in polynomial time and that the smallest read-twice formula equivalent to a given one can be found in polynomial time.read more
Citations
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Learning functions represented as multiplicity automata
TL;DR: A new simple algorithm for learning multiplicity automata with improved time and query complexity is presented, and the learnability of various concept classes is proved, including the class of disjoint DNF and more generally satisfy-O(1) DNF.
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Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries
TL;DR: An incremental output polynomial time algorithm is given for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f, the only method of obtaining information about f through membership queries.
Proceedings ArticleDOI
Learning from a consistently ignorant teacher
TL;DR: A formal model of learning is introduced capturing the idea that teachers may have gaps in their knowledge, and it is shown that knowledge gaps make learning conjunctions of Horn clauses as hard as learning DNF.
Proceedings ArticleDOI
Generating all maximal independent sets of bounded-degree hypergraphs
Nina Mishra,Leonard Pitt +1 more
TL;DR: This work shows that any monotone function with a read-k CNF representation can be learned in terms of its DNF representation with membership queries alone in time polynomial in the DNF size and n assuming k is some fixed constant.
Proceedings ArticleDOI
On the limits of proper learnability of subclasses of DNF formulas
TL;DR: This work improves on Aizenstein, Hellerstein, and Pitt's negative result for proper learning in the exact model and shows that read-thrice DNF formulas are not properly learnable in the extended PAC model, assuming RP.
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When won't membership queries help?
Dana Angluin,Michael Kharitonov +1 more
TL;DR: It is shown that assuming the intractability of quadratic residues module a composite, inverting RSA encryption, or factoring Blum integers, there is no polynomial time prediction algorithm with membership queries for Boolean formulas, constant depth threshold circuits, 3 ?