The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Learnable classes of categorial grammars
Learnable classes of categorial grammars
Consistent Identification in the Limit of Rigid Grammars from Strings Is NP-hard
ICGI '02 Proceedings of the 6th International Colloquium on Grammatical Inference: Algorithms and Applications
Properties of Language Classes With Finite Elasticity
ALT '93 Proceedings of the 4th International Workshop on Algorithmic Learning Theory
A Parallel Context-Free Derivation Hierarchy
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
ACM Transactions on Algorithms (TALG)
Parameterized Complexity
Hölder norms and a hierarchy theorem for parameterized classes of CCG
ICGI'10 Proceedings of the 10th international colloquium conference on Grammatical inference: theoretical results and applications
Theoretical Computer Science
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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 Florêncio ([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.