On Upper and Lower Bounds on the Length of Alternating Towers [article]

Štěpán Holub, Galina Jirásková, Tomáš Masopust
2014 arXiv   pre-print
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next string in the sequence. It is known that if there are towers of any length, then there also exists an infinite tower. We investigate upper and lower bounds on the length of finite towers between two regular languages with respect to the size of the automata
more » ... presenting the languages in the case there is no infinite tower. This problem is relevant to the separation problem of regular languages by piecewise testable languages.
arXiv:1404.4495v2 fatcat:lvksqohfjnfrlor5ygwg22chie