The complexity of hypotheses in Optimality Theory
نویسنده
چکیده
Given a constraint set with k constraints in the framework of Optimality Theory (OT), what is its capacity as a classification scheme for linguistic data? One useful measure of this capacity is the size of the largest data set (i.e. set of input-output pairs) of which each subset is consistent with a different grammar hypothesis. This metric is known as the Vapnik-Chervonenkis Dimension (VCD) and is a standard complexity measure for concept classes in computational learnability theory. In this work I use the three-valued logic of Elementary Ranking Conditions to show that the VCD of OT with k constraints is k−1. This result establishes that the complexity of Optimality Theory is well behaved as a function of k and that the hardness of OT learning is linear in k for a variety of frameworks that employ probabilistic definitions of learnability.
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