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This paper investigates bounds on the generative capacity of prosodic processes, by focusing on the complexity of recursive prosody in coordination contexts in English (Wagner, 2010). Although all phonological processes and most prosodic processes are computationally regular string languages, we show that recursive prosody is not. The output string language is instead parallel multiple context-free (Seki et al., 1991). We evaluate the complexity of the pattern over strings, and then move on to a characterization over trees that requires the expressivity of multi bottom-up tree transducers. In doing so, we provide a foundation for future mathematically grounded investigations of the syntax-prosody interface. 

The subregular approach has revealed that the phonological surface patterns found in natural language are much simpler than previously assumed. Most patterns belong to the subregular class of tier-based strictly local languages (TSL), which characterizes them as the combination of a strictly local dependency with a tier-projection mechanism that masks out irrelevant segments. Some non-TSL patterns have been pointed out in the literature, though. We show that these outliers can be captured by rendering the tier projection mechanism sensitive to the surrounding structure. We focus on a specific instance of these structure-sensitive TSL languages: input-local TSL (ITSL), in which the tier projection may distinguish between identical segments that occur in different local contexts in the input string. This generalization of TSL establishes a tight link between tier-based language classes and ISL transductions, and is motivated by several natural language phenomena.