This paper characterizes a subclass of subsequential string-to-string functions called Output Strictly Local (OSL) and presents a learning algorithm which provably learns any OSL function in polynomial time and data. This algorithm is more efficient than other existing ones capable of learning this class. The OSL class is motivated by the study of the nature of string-to-string transformations, a cornerstone of modern phonological grammars.

<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 &amp; Papert 1971; Rogers &amp; 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>

In this article, we identify Strict Locality as a strong computational property of a certain class of phonological maps from underlying to surface forms. We show that these maps can be modeled with Input Strictly Local functions, a previously undefined class of subregular relations. These functions extend the conception of locality from the Strictly Local formal languages (recognizers/acceptors) ( McNaughton and Papert 1971 , Rogers and Pullum 2011 , Rogers et al. 2013 ) to maps (transducers/functions) and therefore formalize the notion of phonological locality. We discuss the insights such computational properties provide for phonological theory, typology, and learning.

We define two proper subclasses of subsequential functions based on the concept of Strict Locality (McNaughton and Papert, 1971; Rogers and Pullum, 2011; Rogers et al., 2013) for formal languages. They are called Input and Output Strictly Local (ISL and OSL). We provide an automata-theoretic characterization of the ISL class and theorems establishing how the classes are related to each other and to Strictly Local languages. We give evidence that local phonological and morphological processes belong to these classes. Finally we provide a learning algorithm which provably identifies the class of ISL functions in the limit from positive data in polynomial time and data. We demonstrate this learning result on appropriately synthesized artificial corpora. We leave a similar learning result for OSL functions for future work and suggest future directions for addressing non-local phonological processes.

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