Finite-state phonology predicts a typological gap in cyclic stress assignment

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 sub-constituent, starting with the smallest (Chomsky et al. 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; Piggott and Newell, 2005). We claim that, while phonology is sensitive to some aspects of morphological structure, the true constituency is not used, as would be predicted by the phonological cycle: the structure seen by phonology is non-isomorphic to the full morphological structure in the sense of Scheer 2010. Cyclic phonological theories predict that interactions at a distance between prefixes and suffixes can be sensitive to their relative height, as in (1).