Inferring Unions of the Pattern Languages by the Most Fitting Covers
We are interested in learning unions of the pattern languages in the limit from positive data using strategies that guarantee some form of minimality during the learning process. It is known that for any class of languages with so-called finite elasticity, any learning strategy that finds a language that is minimal with respect to inclusion (MINL) ensures identification in the limit. We consider a learning strategy via another form of minimality — the minimality in the number of elements that are shorter than a specified length. A search for languages with this minimality is possible in many cases, and the search can be adapted to identify any class where every language in the class has a characteristic set within the class. We compare solutions using this strategy to those from MINL to illustrate how we may obtain solutions that fulfill both notions of minimality. Finally, we show how the results are relevant using some subclasses of the pattern languages.
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