ISSN:
1573-7470
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract This paper is concerned with the problem of finding a hypothesis in $$\mathcal{T}{\kern 1pt} \mathcal{P}^2 $$ consistent with given positive and negative examples. The hypothesis class $$\mathcal{T}{\kern 1pt} \mathcal{P}^2 $$ 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 $$\mathcal{T}{\kern 1pt} \mathcal{P}^2 $$ . 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 $$\mathcal{T}{\kern 1pt} \mathcal{P}^2 $$ 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 $$\mathcal{T}{\kern 1pt} \mathcal{P}^2 $$ 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 $$\mathcal{T}{\kern 1pt} \mathcal{P}^2 $$ is solved in polynomial time using membership queries.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018912223866
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