  In our previous articles, we have presented a class of endomorphisms of the
Cuntz algebras which are defined by polynomials of canonical generators and
their conjugates. We showed the classification of some case under unitary
equivalence by help of branching laws of permutative representations. In this
article, we construct an automaton which is called the Mealy machine associated
with the endomorphism in order to compute its branching law. We show that the
branching law is obtained as outputs from the machine for the input of
information of a given representation.
