This paper presents two results on the computational expressivity of parallel Optimality Theory (OT) and Harmonic Serialism (HS) (Prince & Smolensky, 1993/2004; McCarthy, 2000) and their sensitivities to different types of markedness constraints. Phonological transformations, i.e., functions that map underlying representations onto surface forms, are computationally regular (Johnson, 1972; Kaplan & Kay, 1994) meaning they are only as expressive as Finite State Transducers (FST). While OT is known to be more computationally expressive, the extent of its expressivity is not known (Heinz, 2018), and the expressivity of HS has only recently been studied (Hao, 2017, 2018). The main result of this paper is that both OT and HS are capable of modeling alphabetical sorting, a process so complex that it requires the use of a Turing Machine. The secondary result is that whether HS overgenerates in this way crucially depends on the type of markedness constraint used. In this particular test case, HS is only able to model alphabetical sorting with global markedness constraints. I hypothesize that Con does not contain global markedness constraints.