This paper expands on Bhaskar et al. (2020)’s result by investigating further properties of BMRS transductions, their connection to regular functions, and their applications in natural-langauge phonology. It introduces a syntactic operator over length-preserving BMRS transductions that is equivalent to function composition. Using this operator, this paper offers a proof that BMRs transductions without predecessor/successor restrictions describe exactly the regular functions. Additionally, it demonstrates applications of BMRS composition to modeling phonological process interactions.