Long-distance phonological processes as tier-based strictly local functions

Whether we analyze phonological processes using a system of rules or constraints, the resulting map from underlying representations to surface pronunciations can be characterized as a function. Viewing processes as mathematical objects in this way allows us to study properties of phonology that hold no matter how it is implemented. Work in this vein has found that a majority of phonological processes only consider information within a finite window, placing them in the highly restrictive class of Strictly Local (SL) functions (Chandlee 2014; Chandlee et al. 2014; 2015). Long-distance phonological processes, however, lie outside the capabilities of the SL functions since they consider information that can be arbitrarily distant. The more powerful class of subsequential functions has been offered as a potential characterization of long-distance phonology (Heinz & Lai 2013; Luo 2017; Payne 2017), but we argue that an intermediate class offers a more natural model. Specifically, by incorporating an autosegmental tier (e.g., Goldsmith 1976) into the structure of an SL function, the non-local information crucial for applying long- distance processes can be rendered local. In addition to assessing the typological coverage of these Tier-based Strictly Local functions (Burness & McMullin 2019; Hao & Andersson 2019; Hao & Bowers 2019), we show that they fail to generate two pathological behaviours (minimum distance requirements and modulo counting) that can be accomplished with a subsequential function. We therefore conclude that tier-based computation is a better characterization of long-distance phonology than subsequential computation.