Cognitive and Sub-regular Complexity

Rogers, John H.; Heinz, Jeffrey; Fero, Margaret; Hurst, Jeremy; Lambert, Dakotah; Wibel, Sean

doi:10.1007/978-3-642-39998-5_6

Cited by 102 publications

(90 citation statements)

References 17 publications

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“…This approach has its roots in finite model theory (Enderton, 2001;Hedman, 2004;Courcelle & Engelfriet, 2012). (See Potts & Pullum (2002) and Rogers et al (2013) for model-theoretic approaches to phonology.) A relational structure contains a set of domain elements and a fixed number of relations over this set.…”

Section: Representing Candidatesmentioning

confidence: 99%

A formal analysis of Correspondence Theory

Payne

Heinz

2017

AMP

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This paper provides a computational analysis of the complexity of GEN and Correspondence Theory in terms of the nature of the logic involved in their formulation. The first result of this analysis shows that the GEN function is not definable in Monadic Second Order (MSO) logic. Second, we show that the set of input-output Correspondence-theoretic candidates from a given underlying representation is definable in First Order (FO) logic, which is less complex than MSO-logic. Third, we present some case studies where the correct input-output Correspondence-theoretic candidate from a given underlying representation can be accomplished with FO-definable, language-specific, inviolable constraints without recourse to optimization.

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Section: Representing Candidatesmentioning

confidence: 99%

A formal analysis of Correspondence Theory

Payne

Heinz

2017

AMP

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“…For example, *NC is a Strictly 2-Local constraint. See Rogers & Pullum (2011) and Rogers et al (2010Rogers et al ( , 2013 for details of these and other subregular languages. A formal definition of ISL functions similar to the informal one above is provided in Chandlee et al (2014), where mathematical relationships to the Strictly Local languages are explained and studied in more detail than we can provide here.…”

Section: Phonological Mapsmentioning

confidence: 99%

Learning Repairs for Marked Structures

Chandlee

Jardine

Heinz

2016

AMP

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“…However, there is a well-studied hierarchy of sub-regular languages (McNaughton & Papert, 1971;Rogers & Pullum, 2011;Rogers et al, 2013), shown in Figure 3, that better capture the kinds of phonotactic patterns we observe in natural language (Heinz, 2009(Heinz, , 2010. At the very bottom of the sub-regular hierarchy lies the Strictly Local (SL) class of languages, which can be defined with grammars of permissible substrings of a certain length k. Consider the language in (5), which represents the allowable surface forms in a language with word-final obstruent devoicing.…”

Section: Strictly Local Functionsmentioning

confidence: 99%

“…On the other hand, the 'multiples of three a's' pattern in 3 is provably not Strictly Local for any value of k (see Rogers & Pullum (2011) and Rogers et al (2013) for details). In the next section, we extend this conception of locality to mappings.…”

Section: Strictly Local Functionsmentioning

confidence: 99%

Learning Phonological Mappings by Learning Strictly Local Functions

Chandlee

Jardine

2014

AMP

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<p>In this paper we identify strict locality as a defining computational property of the input-output mapping that underlies local phonological processes. We provide an automata-theoretic characterization for the class of Strictly Local functions, which are based on the well-studied Strictly Local formal languages (McNaughton & Papert 1971; Rogers & Pullum 2011; Rogers et al. 2013), and show how they can model a range of phonological processes. We then present a learning algorithm, the SLFLA, which uses the defining property of strict locality as an inductive principle to learn these mappings from finite data. The algorithm is a modification of an algorithm developed by Oncina et al. (1993) (called OSTIA) for learning the class of subsequential functions, of which the SL functions are a proper subset. We provide a proof that the SLFLA learns the class of SL functions and discuss these results alongside previous studies on using OSTIA to learn phonological mappings (Gildea and Jurafsky 1996).</p>

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Cognitive and Sub-regular Complexity

Cited by 102 publications

References 17 publications

A formal analysis of Correspondence Theory

A formal analysis of Correspondence Theory

Learning Repairs for Marked Structures

Learning Phonological Mappings by Learning Strictly Local Functions

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