  Takai proposed a method for constructing a maximally permissive supervisor
for the similarity control problem (IEEE Transactions on Automatic Control,
66(7):3197-3204, 2021). This paper points out flaws in his results by providing
a counterexample. Inspired by Takai's construction, the notion of a (saturated)
(G, R)-automaton is introduced and metatheorems concerning (maximally
permissive) supervisors for the similarity control problem are provided in
terms of this notion. As an application of these metatheorems, the flaws in
Takai's work are corrected.
