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String Extension Learning
, 2009
"... This paper defines a collection of functions which define classes of languages, which have the property that they are identifiable in the limit from positive data from a very simple kind of learner. Furthermore these learners are always incremental, maximally consistent, and locally conservative. Th ..."
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This paper defines a collection of functions which define classes of languages, which have the property that they are identifiable in the limit from positive data from a very simple kind of learner. Furthermore these learners are always incremental, maximally consistent, and locally conservative. They are also efficient provided the function itself is efficient. These learners are called string extension learners because components of the grammar are read directly from strings in the language via the defining function. A number of classes of languages in the literature can be described this way including varieties of kLocally Testable languages (McNaughton and Papert 1971) and kPiecewise Testable languages (Simon 1975), as well as some classes not discussed in the literature, such as the kPiecewise Testable languages in the Strict Sense. Potential applications of string extension learning exist for models of natural languages, particularly phonotactics, aspects of cognition and natural language processing.
Computational Phonology – Part I: Foundations
, 2010
"... Computational phonology approaches the study of sound patterns in the world’s languages from a computational perspective. This article explains this perspective and its relevance to phonology. A restrictive, universal property of phonological patterns— they are regular—is established, and the hypoth ..."
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Computational phonology approaches the study of sound patterns in the world’s languages from a computational perspective. This article explains this perspective and its relevance to phonology. A restrictive, universal property of phonological patterns— they are regular—is established, and the hypothesis that they are subregular is presented. This article is intended primarily for phonologists who are curious about computational phonology, but do not have a rigorous background in mathematics or computation. However, it is also informative for readers with a background in computation and the basics of phonology, and who are curious about what computational analysis offers phonological theory. 1 What is Computational Phonology? Computational phonology is formal phonology, and formal phonology is theoretical phonology. Computational phonology is not concerned with the implementation of phonological theories on computers (though that may be a byproduct of computational analysis). The primary concern of computational phonology is the content of the theory itself. Computational Phonology – Part I: Foundations
Learning Subregular Classes of Languages with Factored Deterministic Automata
"... This paper shows how factored finitestate representations of subregular language classes are identifiable in the limit from positive data by learners which are polytime iterative and optimal. These representations are motivated in two ways. First, the size of this representation for a given regular ..."
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This paper shows how factored finitestate representations of subregular language classes are identifiable in the limit from positive data by learners which are polytime iterative and optimal. These representations are motivated in two ways. First, the size of this representation for a given regular language can be exponentially smaller than the size of the minimal deterministic acceptor recognizing the language. Second, these representations (including the exponentially smaller ones) describe actual formal languages which successfully model natural language phenomenon, notably in the subfield of phonology. 1
Cognitive and SubRegular Complexity
"... Abstract. We present a measure of cognitive complexity for subclasses of the regular languages that is based on modeltheoretic complexity rather than on description length of particular classes of grammars or automata. Unlikedescriptionlengthapproaches,thiscomplexitymeasure is independent of the im ..."
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Abstract. We present a measure of cognitive complexity for subclasses of the regular languages that is based on modeltheoretic complexity rather than on description length of particular classes of grammars or automata. Unlikedescriptionlengthapproaches,thiscomplexitymeasure 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. 1
Computational Phonology – Part II: Grammars, Learning, and the Future
, 2010
"... Computational phonology studies sound patterns in the world’s languages from a computational perspective. This article shows that the similarities between different generative theories outweigh the differences, and discusses stochastic grammars and learning models within phonology from a computation ..."
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Computational phonology studies sound patterns in the world’s languages from a computational perspective. This article shows that the similarities between different generative theories outweigh the differences, and discusses stochastic grammars and learning models within phonology from a computational perspective. Also, it shows how the hypothesis that all sound patterns are subregular can be investigated, pointing the direction for future research. Taken together, these contributions show computational phonology is identifying stronger and stronger universal properties of phonological patterns, which are reflected in the grammatical formalisms phonologists employ. This article is intended primarily for phonologists who are curious about computational phonology, but do not have a rigorous background in mathematics or computation. However, it is also informative for readers with a background in computation and the basics of phonology, and who are curious about what computational analysis offers phonological theory. 1
An algebraic characterization of strictly piecewise languages
 In The 8th Annual Conference on Theory and Applications of Models of Computation
, 2011
"... Abstract. This paper provides an algebraic characterization of the Strictly Piecewise class of languages studied by Rogers et al. 2010. These language are a natural subclass of the Piecewise Testable languages (Simon 1975) and are relevant to natural language. The algebraic characterization highligh ..."
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Abstract. This paper provides an algebraic characterization of the Strictly Piecewise class of languages studied by Rogers et al. 2010. These language are a natural subclass of the Piecewise Testable languages (Simon 1975) and are relevant to natural language. The algebraic characterization highlights a similarity between the Strictly Piecewise and Strictly Local languages, and also leads to a procedure which can decide whether a regular language L is Strictly Piecewise in polynomial time in the size of the syntactic monoid for L. 1
Maximum Likelihood Estimation of Featurebased Distributions
"... Motivated by recent work in phonotactic learning (Hayes and Wilson 2008, Albright 2009), this paper shows how to define featurebased probability distributions whose parameters can be provably efficiently estimated. The main idea is that these distributions are defined as a product of simpler distri ..."
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Motivated by recent work in phonotactic learning (Hayes and Wilson 2008, Albright 2009), this paper shows how to define featurebased probability distributions whose parameters can be provably efficiently estimated. The main idea is that these distributions are defined as a product of simpler distributions (cf. Ghahramani and Jordan 1997). One advantage of this framework is it draws attention to what is minimally necessary to describe and learn phonological feature interactions in phonotactic patterns. The “bottomup” approach adopted here is contrasted with the “topdown ” approach in Hayes and Wilson (2008), and it is argued that the bottomup approach is more analytically transparent. 1
Culminativity times harmony equals unbounded stress
, 2012
"... Wellstudied computational representations of stress patterns are desirable in phonological analysis for several reasons. Perhaps the most important one is that they reveal insights which are (1) relevant to any particular theory of phonology and (2) otherwise difficult to divine. This is because th ..."
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Wellstudied computational representations of stress patterns are desirable in phonological analysis for several reasons. Perhaps the most important one is that they reveal insights which are (1) relevant to any particular theory of phonology and (2) otherwise difficult to divine. This is because these representations highlight the importance
What complexity differences reveal about domains in language
, 2012
"... An important distinction between phonology and syntax has been overlooked. All phonological patterns belong to the regular region of the Chomsky Hierarchy but not all syntactic patterns do. We argue that the hypothesis that humans employ distinct learning mechanisms for phonology and syntax currentl ..."
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An important distinction between phonology and syntax has been overlooked. All phonological patterns belong to the regular region of the Chomsky Hierarchy but not all syntactic patterns do. We argue that the hypothesis that humans employ distinct learning mechanisms for phonology and syntax currently offers the best explanation for this difference. 1 A role for phonology in cognitive science Whenitcomestotheproblemofhowhumanslearnlanguage, itappearsmanycomputational learning theorists, cognitive scientists, and psychologists are primarily occupied with the problem of how humans learn to put words and morphemes together to form sentences. In this article we argue that a further understanding of how sounds are put together to form words also bears directly on fundamental questions in cognitive science. In particular, we argue that computational analysis of the typology of patterns in phonology, when compared to the typology of patterns in syntax, reveals that cognitive learning mechanisms are likely multiple and modular in nature. The skew that many researchers exhibit towards morphosyntax may really be a skew towards studying meaning. But we believe that it is because phonological systems impose different sound patterns in different languages without contributing to meaning that they are especially interesting. That is, phonology is about “Rules without Meaning ” in Frits Staal’s (1989) terms. We also believe that an apparent lack of teleological purpose in phonology is what lessens its appeal to the outside. A good discussion of the strangeness of studying phonology is provided inKaye (1989)where he considers what a programming languagelike BASIC would The authors thank Jim Rogers for valuable discussion and an anonymous reviewer and Nick Chater for