Monotone term decision lists

We introduce a new representation class of Boolean functions ? monotone term decision lists ? which combines compact representation size with tractability of essential operations. We present many properties of the class which make it an attractive alternative to traditional universal representation classes such as DNF formulas or decision trees. We study the learnability of monotone term decision lists in the exact model of equivalence and membership queries. We show that, for any constant k?0, k-term monotone decision lists are exactly and properly learnable with nO(k) membership queries in nO(k3) time. We also show that n?(k) membership queries are necessary for exact learning. In contrast, both k-term monotone decision lists (k?2) and general monotone term decision lists are not learnable with equivalence queries alone. We also show that a subclass of monotone term decision lists (disj-MDL) is learnable with equivalence and membership queries, while neither type of query alone suffices.

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