Finding Consistent Categorial Grammars of Bounded Value: A Parameterized Approach

Kanazawa ([8]) has studied the learnability of several parameterized families of classes of categorial grammars. These classes were shown to be learnable from text, in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar. The time complexity of learning these classes has been studied by Costa Florencio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. in this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. As far as the authors are aware, this is the first such result for learning problems.