PAC-Learning Unambiguous k, l-NTS <= Languages

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.