Graph algorithms and NP-completeness
Graph algorithms and NP-completeness
Identification of unions of languages drawn from an identifiable class
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Polynomial-time learning of very simple grammars from positive data
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
The correct definition of finite elasticity: corrigendum to identification of unions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Parameterized learning complexity
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Handbook of logic in artificial intelligence and logic programming
Learnable classes of categorial grammars
Learnable classes of categorial grammars
Inference of Reversible Languages
Journal of the ACM (JACM)
The syntactic process
Grammar Systems: A Grammatical Approach to Distribution and Cooperation
Grammar Systems: A Grammatical Approach to Distribution and Cooperation
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
On the Height of Syntactical Graphs
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Too Much Can be Too Much for Learning Efficiently
AII '92 Proceedings of the International Workshop on Analogical and Inductive Inference
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
On the logic and learning of language
On the logic and learning of language
ACM Transactions on Algorithms (TALG)
Comparison of some descriptional complexities of 0L systems obtained by a unifying approach
Information and Computation
Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology
Combinatorial Algorithms
Improved upper bounds for vertex cover
Theoretical Computer Science
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
Finding consistent categorial grammars of bounded value: a parameterized approach
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
| Hi-index | 5.23 |
In Kanazawa (1998) [1], the learnability of several parameterized families of categorial grammar classes was studied. These classes were shown to be learnable in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on parameters of the grammars which intuitively correspond to restrictions on linguistic aspects, such as the amount of lexical ambiguity. The time complexity of learning these classes has been studied in Costa Florncio (2003) [2]. It was shown that, for most of these classes, selecting a grammar from the class that is consistent with given data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additionally, parameters are defined that allow FPT-results; roughly, this implies that if these parameters are fixed, these problems become tractable. We also define the new family G"k"-"s"u"m"-"v"a"l, which is natural from the viewpoints of Parameterized Complexity, a flourishing area of Complexity Theory (see Downey and Fellows (1999) [3]) and from Descriptional Complexity, a sub-area of Formal Language Theory (see Holzer and Kutrib (2010) [4]). We prove its learnability, analyze its relation to other classes from the literature and prove a hierarchy theorem. This approach is then generalized to a parameterized family defined in terms of a bound on the descriptional complexity expressed as a Holder norm. We show that both the hierarchy result and the property of finite elasticity (and thus learnability) are preserved under this generalization.