Abstract
This paper characterizes the polynomial time learnability of TP k, the class of collections of at most k first-order terms. A collection in TPA k defines the union of the languages defined by each first-order terms in the set. Unfortunately, the class TP k not polynomial time learnable in most of learning frameworks under standard assumptions in computational complexity theory. To overcome this computational hardness, we relax the learning problem by allowing a learning algorithm to make membership queries. We present a polynomial time algorithm that exactly learns every concept in TP k using O(kn) equivalence and O(k 2 n · max{k, n}) membership queries, where n is the size of longest counterexample given so far. In the proof, we use a technique of replacing each restricted subset query by several membership queries under some condition on a set of function symbols. As corollaries, we obtain the polynomial time PAC-learnability and the polynomial time predictability of TP k when membership queries are available. We also show a lower bound Ω(kn) of the number of queries necessary to learn TP k using both types of queries. Further, we show that neither types of queries can be eliminated to achieve efficient learning of TP k. Finally, we apply our results in learning of a class of restricted logic programs, called unit clause programs.
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© 1995 Springer-Verlag Berlin Heidelberg
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Arimura, H., Ishizaka, H., Shinohara, T. (1995). Learning unions of tree patterns using queries. In: Jantke, K.P., Shinohara, T., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1995. Lecture Notes in Computer Science, vol 997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60454-5_29
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DOI: https://doi.org/10.1007/3-540-60454-5_29
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