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.

We demonstrate a computational restriction on iterative prosody in phonology by using logical transductions. We show that the typology is fundamentally local but requires output recursion, formulated via quantifier-free transductions and least-fixed-point operators, respectively. We focus on two case studies from iterative prosody. One is iterative secondary stress. The other is more complex: iterative syllabification and epenthesis in Arabic dialects. The second case study involves formalizing Ito (1989)'s analysis of directional syllabification.

This paper offers a computational characterization of tone-to-TBU association processes using a restricted least-fixed point logic. Crucially, least fixed point logics allow recursive definitions which capture output-oriented processes. The added requirement that these definitions are quantifier-free ensures that they are inherently local, a restriction that is well-motivated for phonological processes in general. The typology developed here distinguishes between possible and impossible tone mappings, capturing a wider range of attested tone mappings (left-to-right, right-to-left, edge-in, quality-sensitive) than previous rule-based or optimization approaches, while also explaining why certain unattested mapping patterns (for example center-out association) are impossible. This thus represents a strong first approximation of a definition for output-based local functions over non-linear structures

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The metrical foot has a long pedigree as a theoretical device in generative phonology (Liberman & Prince, 1977; Halle & Vergnaud, 1978; Selkirk, 1980; Hammond, 1984; Halle & Vergnaud, 1987; Idsardi, 1992; Hayes, 1995). While the motivations for foot structure are typically studied in terms of stress, this paper provides evidence from the principles of formal language theory (Chomsky, 1956; Hopcroft & Ullman, 1979) for foot-based analyses of non-stress processes. Though use of foot structure in these analyses is not novel (see Gonzalez (2018) for an overview) this paper contributes a precise characterization of what is at stake in terms of the computation of these processes when foot structure is present versus when it is not. This formal computational analysis indicates that feet have measurable implications for the predicted typology of these patterns. Thus, support is provided for a specific substantive phonological proposal based on the well-defined measures of complexity that formal language theory offers.