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Title:The Complexity of Ranking Hypotheses in Optimality Theory
Authors:Jason Riggle
Comment:This cleaned-up version of the paper will appear in Computational Linguistics (sometime soon) and has benefited tremendously from the comments of two anonymous CL reviewers.
Abstract: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 of which each subset is consistent with a different grammar hypothesis. This measure 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 Optimality Theory with k constraints is k-1. Analysis of OT in terms of the VCD establishes that the complexity of OT is a well behaved function of k and that the �hardness� of learning in OT is linear in k for a variety of frameworks that employ probabilistic definitions of learnability.
Type:Paper/tech report
Area/Keywords:Computation,Formal Analysis,Learnability
Article:Version 1