Communications of the ACM
Foundations of deductive databases and logic programming
Computational limitations on learning from examples
Journal of the ACM (JACM)
Polynomial-time inference of arbitrary pattern languages
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Machine learning: a theoretical approach
Machine learning: a theoretical approach
Machine Learning
Machine Learning
Inclusion is Undecidable for Pattern Languages
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Inductive Inference Machines That Can Refute Hypothesis Spaces
ALT '93 Proceedings of the 4th International Workshop on Algorithmic Learning Theory
Learning Unions of Tree Patterns Using Queries
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
A Polynomial Time Algorithm for Finding Finite Unions of Tree Pattern Languages
Proceedings of the Second International Workshop on Nonmonotonic and Inductive Logic
Learning a subclass of regular patterns in polynomial time
Theoretical Computer Science - Algorithmic learning theory
| Hi-index | 0.00 |
This paper is concerned with the problem of finding a hypothesis in \mathcal{TP}^2 consistent with given positive and negative examples. The hypothesis class \mathcal{TP}^2 consists of all sets of at most two tree patterns and represents the class of unions of at most two tree pattern languages. Especially, we consider the problem from the point of view of the consistency problem for \mathcal{TP}^2. The consistency problem is a problem for deciding whether there exists a consistent hypothesis with given positive and negative examples within some fixed hypothesis space. Efficient solvability of that problem is closely related to the possibility of efficient machine learning or machine discovery. Unfortunately, however, the consistency problem is known to be NP‐complete for many hypothesis spaces. In this paper, the problem for the class \mathcal{TP}^2 is also shown to be NP‐complete. In order to overcome this computational hardness, we try to use additional information obtained by making queries. First, we give an algorithm that, using restricted subset queries, solves the consistency problem for \mathcal{TP}^2 in time polynomial in the total size of given positive and negative examples. Next, we show that each subset query made by the algorithm can be replaced by several membership queries under some condition on a set of function symbols. As a result, we have that the consistency problem for \mathcal{TP}^2 is solved in polynomial time using membership queries.