In multilevel parallel Optimality Theory grammars, the number of candidates (possible paths from the input to the output level) increases exponentially with the number of levels of representation. The problem with this is that with the customary strategy of listing all candidates in a tableau, the computation time for evaluation (i.e., choosing the winning candidate) and learning (i.e., reranking the constraints on the basis of language data) increases exponentially with the number of levels as well. This article proposes instead to collect the candidates in a graph in which the number of nodes and the number of connections increase only linearly with the number of levels of representation. As a result, there exist procedures for evaluation and learning that increase only linearly with the number of levels. These efficient procedures help to make multilevel parallel constraint grammars more feasible as models of human language processing. We illustrate visualization, evaluation, and learning with a toy grammar for a traditional case that has already previously been analyzed in terms of parallel evaluation, namely, French liaison.

This article shows that Error-Driven Constraint Demotion (EDCD), an error-driven learning algorithm proposed by Tesar (1995) for Prince and Smolensky's (1993/2004) version of Optimality Theory, can fail to converge to a correct totally ranked hierarchy of constraints, unlike the earlier non-error-driven learning algorithms proposed by Tesar and Smolensky (1993). The cause of the problem is found in Tesar's use of “mark-pooling ties,” indicating that EDCD can be repaired by assuming Anttila's (1997) “permuting ties” instead. Proofs show, and simulations confirm, that totally ranked hierarchies can indeed be found by both this repaired version of EDCD and Boersma's (1998) Minimal Gradual Learning Algorithm.

The Gradual Learning Algorithm (Boersma 1997) is a constraint-ranking algorithm for learning optimality-theoretic grammars. The purpose of this article is to assess the capabilities of the Gradual Learning Algorithm, particularly in comparison with the Constraint Demotion algorithm of Tesar and Smolensky (1993, 1996, 1998, 2000), which initiated the learnability research program for Optimality Theory. We argue that the Gradual Learning Algorithm has a number of special advantages: it can learn free variation, deal effectively with noisy learning data, and account for gradient well-formedness judgments. The case studies we examine involve Ilokano reduplication and metathesis, Finnish genitive plurals, and the distribution of English light and dark /l/.