Iterative Learning from Texts and Counterexamples Using Additional Information
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Date
2009-04-27T01:24:54Z
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Abstract
A variant of iterative learning in the limit is studied when a learner gets negative examples refuting conjectures containing data in excess of the target language and uses additional information of the following four types:
a) memorizing up to n input elements seen so far; b) up to $n$ feedback memberships queries (testing if an item is a member of the input seen so far); c) the number of input elements seen so far; d) the maximal element of the input seen so far.
We explore how additional information available to such learners may help. In particular, we show that adding the maximal element or the number of elements seen so far helps such learners to infer any indexed class of languages class-preservingly (using a descriptive numbering defining the class) --- as it was proved by Jain and Kinber, this is not possible without using additional information.
We also study how, in the given
context, different types of additional information fare agains each other, and establish hierarchies of learners memorizing n+1 versus n input elements seen and n+1 versus n feedback membership queries.