Read-Twice DNF Formulas Are Properly Learnable

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.

Authors

• K. Pillaipakkamnatt
• V. Raghavan

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