Structure Sensitive Tier Projection: Applications and Formal Properties

The subregular approach has revealed that the phonological surface patterns found in natural language are much simpler than previously assumed. Most patterns belong to the subregular class of tier-based strictly local languages (TSL), which characterizes them as the combination of a strictly local dependency with a tier-projection mechanism that masks out irrelevant segments. Some non-TSL patterns have been pointed out in the literature, though. We show that these outliers can be captured by rendering the tier projection mechanism sensitive to the surrounding structure. We focus on a specific instance of these structure-sensitive TSL languages: input-local TSL (ITSL), in which the tier projection may distinguish between identical segments that occur in different local contexts in the input string. This generalization of TSL establishes a tight link between tier-based language classes and ISL transductions, and is motivated by several natural language phenomena.

[1]  Adam Jardine,et al.  Computationally, tone is different* , 2016, Phonology.

[3]  Jane Chandlee,et al.  STRICTLY LOCAL PHONOLOGICAL PROCESSES , 2014 .

[4]  Rémi Eyraud,et al.  Learning Strictly Local Subsequential Functions , 2014, TACL.

[5]  Jeffrey Heinz,et al.  Learning Tier-based Strictly 2-Local Languages , 2016, TACL.

[6]  James Rogers,et al.  On Languages Piecewise Testable in the Strict Sense , 2007, MOL.

[7]  Herbert G. Tanner,et al.  Tier-based Strictly Local Constraints for Phonology , 2011, ACL.

[8]  Alëna Aksënova,et al.  Formal Restrictions On Multiple Tiers , 2018 .

[9]  Kevin McMullin,et al.  Tier-based locality in long-distance phonotactics : learnability and typology , 2016 .

[10]  Connor Mayer,et al.  Sanskrit n-Retroflexion is Input-Output Tier-Based Strictly Local , 2018 .

[11]  Raymond E. Miller,et al.  Varieties of Formal Languages , 1986 .

[12]  Jeffrey Heinz,et al.  The computational nature of phonological generalizations , 2018 .

[13]  James Rogers,et al.  Formal language theory: refining the Chomsky hierarchy , 2012, Philosophical Transactions of the Royal Society B: Biological Sciences.

[14]  James Rogers,et al.  Aural Pattern Recognition Experiments and the Subregular Hierarchy , 2011, J. Log. Lang. Inf..

[15]  Wolfgang Thomas,et al.  Languages, Automata, and Logic , 1997, Handbook of Formal Languages.

[16]  Kevin McMullin,et al.  Efficient Learning of Tier-Based Strictly k-Local Languages , 2017, LATA.

[17]  Thomas Graf.  The power of locality domains in phonology , 2017 .

[18]  Aniello De Santo,et al.  Learning phonotactic restrictions on multiple tiers , 2019 .

[19]  Imre Simon,et al.  Piecewise testable events , 1975, Automata Theory and Formal Languages.

[20]  James Rogers,et al.  Cognitive and Sub-regular Complexity , 2013, FG.

[21]  R. McNaughton,et al.  Counter-Free Automata , 1971 .

[22]  Rachel Walker,et al.  Yaka Nasal Harmony: Spreading or Segmental Correspondence? , 2000 .

[23]  Jie Fu,et al.  An Algebraic Characterization of Strictly Piecewise Languages , 2011, TAMC.

[24]  Larry M. Hyman,et al.  How autosegmental is phonology? , 2013 .

[25]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[26]  Richard Applegate,et al.  Ineseño Chumash Grammar , 1972 .

[27]  Connor Mayer,et al.  A Challenge for Tier-Based Strict Locality from Uyghur Backness Harmony , 2018, FG.

[28]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[29]  Jeffrey Heinz,et al.  Strict Locality and Phonological Maps , 2018, Linguistic Inquiry.

[30]  Janusz A. Brzozowski,et al.  The Dot-Depth Hierarchy of Star-Free Languages is Infinite , 1978, J. Comput. Syst. Sci..