Learning unions of tree patterns using queries

  • Hiroki Arimura
  • Hiroki Ishizaka
  • Takeshi Shinohara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 997)


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(k2n · 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Hiroki Arimura
    • 1
  • Hiroki Ishizaka
    • 1
  • Takeshi Shinohara
    • 1
  1. 1.Department of Artificial IntelligenceKyushu Institute of TechnologyIizukaJapan

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