http://alpha-leonis.lids.mit.edu/wordpress/wp-content/uploads/2014/04/tics-birdsong2011.pdf

Songs to syntax: the linguistics of birdsong

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.).

Learning Long-Distance Phonotactics

The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages).

/pdf/formal-language-theory-refining-the-chomsky-hierarchy-33wnxy2dqk.pdf

Formal language theory: refining the Chomsky hierarchy

We present a measure of cognitive complexity for subclasses of the regular languages that is based on model-theoretic complexity rather than on description length of particular classes of grammars or automata. Unlike description length approaches, this complexity measure is independent of the implementation details of the cognitive mechanism. Hence, it provides a basis for making inferences about cognitive mechanisms that are valid regardless of how those mechanisms are actually realized.

/pdf/cognitive-and-sub-regular-complexity-2ezk5d83nw.pdf

Cognitive and Sub-regular Complexity

Beginning with Goldsmith (1976), the phonological tier has a long history in phonological theory to describe non-local phenomena. This paper defines a class of formal languages, the Tier-based Strictly Local languages, which begin to describe such phenomena. Then this class is located within the Subregular Hierarchy (McNaughton and Papert, 1971). It is found that these languages contain the Strictly Local languages, are star-free, are incomparable with other known sub-star-free classes, and have other interesting properties.

Tier-based Strictly Local Constraints for Phonology

In this paper we explore the class of Strictly Piecewise languages, originally introduced to characterize long-distance phonotactic patterns by Heinz [7] as the Precedence Languages. We provide a series of equivalent abstract characterizations, discuss their basic properties, locate them relative to other well-known subregular classes and provide algorithms for translating between the grammars defined here and finite state automata as well as an algorithm for deciding whether a regular language is Strictly Piecewise.

Gil Bailey

Papers

On languages piecewise testable in the strict sense