In this article, we identify Strict Locality as a strong computational property of a certain class of phonological maps from underlying to surface forms. We show that these maps can be modeled with Input Strictly Local functions, a previously undefined class of subregular relations. These functions extend the conception of locality from the Strictly Local formal languages (recognizers/acceptors) ( McNaughton and Papert 1971 , Rogers and Pullum 2011 , Rogers et al. 2013 ) to maps (transducers/functions) and therefore formalize the notion of phonological locality. We discuss the insights such computational properties provide for phonological theory, typology, and learning.

This article shows that specific properties of long-distance phonotactic patterns derived from consonantal harmony patterns (Hansson 2001, Rose and Walker 2004) follow from a learner that generalizes only on the basis of the order of sounds, not the distance between them. The proposed learner is simple, efficient, and provably correct, and does not require an a priori notion of tier or projection (contra the model in Hayes and Wilson 2008); nor does it rely on the additional structure provided by Optimality Theory grammars (Prince and Smolensky 1993, 2004) or grammars in the principles-and-parameters framework (Chomsky 1981, Dresher and Kaye 1990, Gibson and Wexler 1994). Not only does the noncounting nature of nonlocal dependencies automatically follow from the way the learner generalizes, it also explains the absence of blocking patterns from the typology. Finally, the learner lends support to the idea that long-distance phonotactic patterns are phenomenologically distinct from spreading patterns, contra the hypothesis of Strict Locality (Gafos 1999, et seq.).

Idsardi (2006) claims that Optimality Theory (OT; Prince and Smolensky 1993, 2004) is “in general computationally intractable” on the basis of a proof adapted from Eisner 1997a. We take issue with this conclusion on two grounds. First, the intractability result holds only in cases where the constraint set is not fixed in advance (contra usual definitions of OT), and second, the result crucially depends on a particular representation of OT grammars. We show that there is an alternative representation of OT grammars that allows for efficient computation of optimal surface forms and provides deeper insight into the sources of complexity of OT. We conclude that it is a mistake to reject OT on the grounds that it is computationally intractable.