Since Halle (1962), explicit algebraic variables (often called alpha notation) have been commonplace in phonological theory. However, Hayes and Wilson (2008) proposed a variable-free model of phonotactic learning, sparking a debate about whether such algebraic representations are necessary to capture human phonological acquisition. While past experimental work has found evidence that suggested a need for variables in models of phonology (Berent et al. 2012, Moreton 2012, Gallagher 2013), this

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... per presents a novel mechanism, Probabilistic Feature Attention (PFA), that allows a variable-free model of phonotactics to predict a number of these phenomena. Additionally, experimental results involving phonological generalization that cannot be explained by variables are captured by this novel approach. These results cast doubt on whether variables are necessary to capture human-like phonotactic learning and provide a useful alternative to such representations.