The fact that Parsing and Generation share the same grammatical knowledge is often considered the null hypothesis (Momma and Phillips 2018) but very few algorithms can take advantage of a cognitively plausible incremental procedure that operates roughly in the way words are produced and understood in real time. This is especially difficult if we consider cross-linguistic variation that has a clear impact on word order. In this paper, I present one such formalism, dubbed Expectation-based Minimalist Grammar (e-MG), that qualifies as a simplified version of the (Conflated) Minimalist Grammars, (C)MGs (Stabler 1997, 2011, 2013), and Phase-based Minimalist Grammars, PMGs (Chesi 2005, 2007; Stabler 2011). The crucial simplification consists of driving structure building only using lexically encoded categorial top-down expectations. The commitment to the top-down procedure (in e-MGs and PMGs, as opposed to (C)MGs, ) will be crucial to capture a relevant set of empirical asymmetries in a parameterized cross-linguistic perspective which represents the least common denominator of structure building in both Parsing and Generation
