Consistent identification in the limit of rigid grammars from strings is NP-hard

Abstract

In [Bus87] and [BP90] some 'discovery procedures' for classical categorial grammars were defined. These procedures take a set of structures (strings labeled with derivational information) as input and yield a set of hypotheses in the form of grammars. In [Kan98] learning functions based on these discovery procedures were studied, and it was shown that some of the classes associated with these functions can be identified in the limit (i.e. are learnable) from strings, by a computable function. The time complexity of these functions however was still left an open question. In this paper we will show that the learning functions for these learnable classes are all NP-hard.