On the Complexity of the Problem of the Acquisition of Phonotactics in Optimality Theory

The problem of the acquisition of phonotactics in Optimality Theory is formulated as the problem of learning a ranking consistent with a finite set of data that furthermore corresponds to a smallest (w.r.t. set inclusion) language. The paper focuses on the universal formulation of the problem, whereby generating function and constraint set vary arbitrarily as inputs of the problem. It is shown that the universal problem of the acquisition of phonotactics in OT is not-solvable (NP-complete), even when we take the time to list all candidates. This result motivates a nonuniversalistic approach to the problem of the acquisition of phonotactics, whereby the problem is restricted to specific families of generating functions and constraint sets and solution algorithms are allowed to take advantage of the peculiar properties of these families.