Linguists disagree on whether morphological representations should be strings or trees. We argue that tree-based views of morphology can provide new insights into morphological complexity even in cases where the posited tree structure closely matches the surface string. Our argument is based on a subregular case study of morphologically conditioned allomorphy, where the phonological form of some morpheme (the target) is conditioned by the presence of some other morpheme (the trigger) somewhere within the morphosyntactic context. The trigger and target can either be linearly adjacent or non-adjacent, and either the trigger precedes the target (inwardly sensitive) or the target precedes the trigger (outwardly sensitive). When formalized as string transductions, the only complexity difference is between local and non-local allomorphy. Over trees, on the other hand, we also see a complexity difference between inwardly sensitive and outwardly sensitive allomorphy. Just as unboundedness assumptions can sometimes tease apart patterns that are equally complex in the finitely bounded case, tree-based representations can reveal differences that disappear over strings.

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.

Sanskrit /n/-retroflexion is one of the most complex segmental processes in phonology. While it is still star-free, it does not fit in any of the subregular classes that are commonly entertained in the literature. We show that when construed as a phonotactic dependency, the process fits into a class we call input-output tier-based strictly local (IO-TSL), a natural extension of the familiar class TSL. IO-TSL increases the power of TSL’s tier projection function by making it an input-output strictly local transduction. Assuming that /n/-retroflexion represents the upper bound on the complexity of segmental phonology, this shows that all of segmental phonology can be captured by combining the intuitive notion of tiers with the independently motivated machinery of strictly local mappings.