In this squib, we start from the empirical generalization that phonological grammars are all within the computational power of finite-state devices, a position nearly universally accepted in computational phonology. We show that this rules out certain patterns of morphologically sensitive stress assignment that are predicted by the phonological cycle hypothesis.
Given that morphological structure is hierarchical in complex words, the phonological cycle proposes that the phonological grammar reapplies successively to each morphological subconstituent, starting with the smallest (Chomsky, Halle, and Lukoff 1956, Chomsky and Halle 1968). Variants on this basic idea have been widely influential in phonological theory, including versions with a Strict Cycle Condition (Kean 1974, Mascaró 1976), versions that group constituents into strata (Kiparsky 2000, Bermúdez-Otero 2011), and versions that make reference to phases (Marvin 2002, Newell and Piggott 2014). We claim that, while phonology is sensitive...