We revisit the following lower bound methods for the size of a nondeterministic finite automaton: the fooling set technique, the extended fooling set technique, and the biclique edge cover technique, presenting these methods in terms of quotients and atoms of regular languages. Although the lower bounds obtained by these methods are not necessarily tight, some classes of languages for which tight bounds can be achieved, are known. We show that languages with maximal reversal complexity belong to the class of languages for which the fooling set technique provides a tight bound. We also show that the extended fooling set technique is tight for a subclass of unary cyclic languages.
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