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What is known about the phonological constraints limiting the form of a Semitic (or even Afroasiatic) root? In other words, are there any limits to the possible sequences of radicals?

For example, per Daya, E., Roth, D., & Wintner, S. (2008). Identifying Semitic roots: Machine learning with linguistic constraints. Computational Linguistics, 34(3), 429-448, the coincidence of the first and second consonants is extremely rare compared to the similarity of 2nd and 3rd. Are there more patterns which allow to predict whether the given C-C-C form (or not threeconsonantal) can be a root, such as some hierarchy of sonority followed, or some sequences banned to avoid their possible contacts when there is no vowel in-between?

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The classic original study is Joseph Greenberg 1950 "The Patterning of Root Morphemes in Semitic" (Word 5, 162–181). A later study with a larger lexicon was conducted by M. Mrayati 1987 "Statistical studies of Arabic language roots". The OCP controversy features this pattern prominently. There are different degrees of strength to the particular effects, for example as far as I know, in a triconsonantal root there are no roots with s and z (either order) as C2 and C3. The overall picture is that if you just look at the frequency of certain phonemes in the lexicon of roots, you find that m occurs a certain number of times, likewise b, n, k... but when you looc at co-ocurrrence (b plus k vs. b plus m), there is a decreased likelihood of finding b and m together in a root. The effect that has been of interest to theorists is the treatment of absolutely identical consonants (where the limits are extremely strong) and homorganic consonants. Greenberg spells out the facts in great detail.

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