2010 | OriginalPaper | Buchkapitel
PAC-Learning Unambiguous k,l-NTS ≤ Languages
verfasst von : Franco M. Luque, Gabriel Infante-Lopez
Erschienen in: Grammatical Inference: Theoretical Results and Applications
Verlag: Springer Berlin Heidelberg
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In this paper we present two hierarchies of context-free languages: The
k
,
l
-NTS languages and the
k
,
l
-NTS
≤
languages.
k
,
l
-NTS languages generalize the concept of Non-Terminally Separated (NTS) languages by adding a fixed size context to the constituents, in the analog way as
k
,
l
-substitutable languages generalize substitutable languages (Yoshinaka, 2008).
k
,
l
-NTS
≤
languages are
k
,
l
-NTS languages that also consider the edges of sentences as possible contexts. We then prove that Unambiguous
k
,
l
-NTS
≤
(
k
,
l
-UNTS
≤
) languages be converted to plain old UNTS languages over a richer alphabet. Using this and the result of polynomial PAC-learnability with positive data of UNTS grammars proved by Clark (2006), we prove that
k
,
l
-UNTS
≤
languages are also PAC-learnable under the same conditions.