Abstrakt
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. We study upper and lower bounds on the number of words in maximal finite towers between two regular languages with respect to the size of the NFA (respectively the DFA) representation.
We show that the upper bound is polynomial in the number of states and exponential in the size of the alphabet, and that it is asymptotically tight if the size of the alphabet is fixed. If the alphabet may grow with the number of states of the automata, the lower bound on the height of towers is exponential with respect to that number.
In this case the asymptotically optimal bound remains an open problem. Since, in many cases, the constructed towers are sequences of prefixes, we also study towers of prefixes. (C) 2019 Elsevier Inc.
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