We consider a variant of Gold’s learning paradigm where a learner receives as input n different languages (in form of one text where all input languages are interleaved). Our goal is to explore the situation when a more “coarse” classification of input languages is possible, whereas more refined classification is not. More specifically, we answer the following question: under which conditions, a learner, being fed n different languages, can produce m grammars covering all input languages, but cannot produce k grammars covering input languages for any k > m. We also consider a variant of this task, where each of the output grammars may not cover more than r input languages. Our main results indicate that the major factor affecting classification capabilities is the difference n − m between the number n of input languages and the number m of output grammars. We also explore relationship between classification capabilities for smaller and larger groups of input langu...
Sanjay Jain, Efim B. Kinber