A cyclic unary regular language is a regular language over a unary alphabet that is represented
by a cyclic automaton. We propose a similarity measure for cyclic unary regular
languages by modifying the Jaccard similarity coe cient and the So rensen coe cient to
measure the level of overlap between such languages. This measure computes the proportion
of strings that are shared by two or more cyclic unary regular languages and is
an upper bound of the Jaccard coe cient and the S orensen coe cient. By using such
similarity measure, we de ne a dissimilarity measure for cyclic unary regular languages
that is a semimetric distance. Moreover, it can be used for the non-cyclic case.
