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The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We prove that n! and ⌊e(n − 1)!⌋ are tight upper bounds for the syntactic complexity of Rand J -trivial regular languages, respectively.doi:10.1142/s0129054114400097 fatcat:levq7nx7rffavgmfsgsy44uocu