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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 Jeffrey Heinz Chetan Rawal and Herbert G. Tanner University of Delaware heinz rawal btanner@udel.edu Abstract 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. 1 Introduction The phonological tier is a level of representation where not all speech sounds are present. For example the vowel tier of the Finnish word paivaa Hello is simply the vowels in order without the consonants aiaa. Tiers were originally introduced to describe tone systems in languages Goldsmith 1976 and subsequently many variants of the theory were proposed Clements 1976 Vergnaud 1977 McCarthy 1979 Poser 1982 Prince 1984 Mester 1988 Odden 1994 Archangeli and Pulleyblank 1994 Clements and Hume 1995 . Although these theories differ in their details they each adopt the premise that representational levels exist which exclude certain speech sounds. Computational work exists which incorporates and formalizes phonological tiers Kornai 1994 Bird 1995 Eisner 1997 . There are also learning algorithms which employ them Hayes and Wilson 2008 Goldsmith and Riggle to appear . However there is no work of which the authors are aware that 58 addresses the expressivity or properties of tier-based patterns in terms of formal language theory. This paper begins to fill this gap by defining TierBased Strictly Local TSL languages which generalize the Strictly Local languages McNaughton and Papert 1971 . It is shown that TSL languages are necessarily star-free but are incomparable with other known .
