27 research outputs found
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Information-theoretic Characterization of the Sub-regular Hierarchy
Our goal is to link two different formal notions of complexity: the complexity classes defined by Formal Language Theory (FLT)—in particular, the Sub-regular Hierarchy (Rogers et al., 2013; Lai, 2015; Heinz, 2018)—and Statistical Com- plexity Theory (Feldman and Crutchfield, 1998; Crutchfield and Marzen, 2015). The motivation for exploring this connection is that factors involving memory resources have been hypothesized to explain why phonological processes seem to inhabit the Sub-regular Hierarchy, and Statistical Complexity Theory gives an information-theoretic characterization of memory use. It is currently not known whether statistical complexity and FLT define equivalent complexity classes, or whether statistical complexity cross-cuts the usual FLT hierarchies. Our work begins to bridge the gap between FLT and Information Theory by presenting characterizations of certain Sub-regular languages in terms of statistical complexit
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Metrical Grids and Generalized Tier Projection
This paper formalizes metrical grid theory (MGT, Prince, 1983; Hayes, 1995) and studies its expressive power. I show that MGT analyses of a certain form can describe stress systems beyond the input tier-based input strictly local functions proposed by Hao and Andersson (2019), but conjecture that such analyses do not describe systems beyond the input tier-based strictly local languages of Baek (2018). These results reveal fundamental differences between the three formalisms
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A Logical and Computational Methodology for Exploring Systems of Phonotactic Constraints
We introduce a methodology built around a logical analysis component based on a hierarchy of classes of Subregular constraints characterized by the kinds of features of a string a mechanism must be sensitive to in order to determine whether it satisfies the constraint, and a computational component built around a publicly-available interactive workbench that implements, based on the equivalence between logical formulae and finite-state automata, a theorem prover for these logics (even algorithmically extracting certain classes of constraints), wherein the alternation between these logical and computational analyses can provide useful insight more easily than using either in isolation
The computational nature of stress assignment
While computational studies of stress patterns as phonotactics have yielded restrictive characterizations of stress (Rogers et al., 2013) with provably correct learning procedures (Heinz, 2009), an outstanding question is the nature of stress assignment as a function which assigns stress to an underlying bare string of syllables. This paper fills this gap by locating stress patterns with respect to the subsequential class of functions (Mohri, 1997), which are argued to be important for phonology in that the vast majority of phonological functions fall within the subsequential boundary (Heinz & Lai, 2013; Chandlee, 2014), with the notable exception of tone and vowel harmony (Jardine, 2016; McCollum et al., under review). The main result is that – while most, if not all quantity insensitive (QI) stress systems are subsequential functions – the same does not hold for quantity sensitive (QS) systems. Counter-intuitively, so-called default-to-opposite QS patterns are subsequential, but default-to-same QS patterns are provably not. It also supports the claim of Jardine (2016) that certain tonal patterns are non-sequential because their suprasegmental nature allows for more a more powerful computation. As stress assignment is also suprasegmental, the existence of non-sequential stress functions adds evidence for this conclusion