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A tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word. The height of the tower is the number of words in the sequence. If there is no infinite tower (a tower of infinite height), then the height of all towers between the languages is bounded. We study upper and lower bounds on the height of maximal finite towers between two regular languages with respect to the size of the NFA (respectively the DFA) representation.doi:10.1016/j.ic.2019.01.004 fatcat:cis3qcln6rfrdpnc4przjccnqq