Easy and Hard Constraint Ranking in OT: Algorithms and Complexity
Abstract
We consider the problem of ranking a set of OT constraints in a manner consistent with data. We speed up Tesar and Smolensky's RCD algorithm to be linear on the number of constraints. This finds a ranking so each attested form x_i beats or ties a particular competitor y_i. We also generalize RCD so each x_i beats or ties all possible competitors. Alas, this more realistic version of learning has no polynomial algorithm unless P=NP! Indeed, not even generation does. So one cannot improve qualitatively upon brute force: Merely checking that a single (given) ranking is consistent with given forms is coNPcomplete if the surface forms are fully observed and Delta_2^pcomplete if not. Indeed, OT generation is OptPcomplete. As for ranking, determining whether any consistent ranking exists is coNPhard (but in Delta_2^p) if the forms are fully observed, and Sigma_2^pcomplete if not. Finally, we show that generation and ranking are easier in derivational theories: in P, and NPcomplete.
 Publication:

arXiv eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:cs/0102019
 Bibcode:
 2001cs........2019E
 Keywords:

 Computer Science  Computation and Language;
 Computer Science  Computational Complexity;
 I.2.7;
 F.2.2
 EPrint:
 12 pages, online proceedings version (small corrections and clarifications to printed version)