Learning Relational Patterns
Patterns provide a simple, yet powerful means of describing formal languages. However, for many applications, neither patterns nor their generalized versions of typed patterns are expressive enough. This paper extends the model of (typed) patterns by allowing relations between the variables in a pattern. The resulting formal languages are called Relational Pattern Languages (RPLs). We study the problem of learning RPLs from positive data (text) as well as the membership problem for RPLs. These problems are not solvable or not efficiently solvable in general, but we prove positive results for interesting subproblems.
We further introduce a new model of learning from a restricted pool of potential texts. Probabilistic assumptions on the process that generates words from patterns make the appearance of some words in the text more likely than that of other words. We prove that, in our new model, a large subclass of RPLs can be learned with high confidence, by effectively restricting the set of likely candidate patterns to a finite set after processing a single positive example.
KeywordsPolynomial Time Recursive Relation Formal Language Target Language Regular Language
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