  Finite cellular automata (FCA) are widely used in simulating nonlinear
complex systems, and their reversibility is closely related to information loss
during the evolution. However, only a relatively small portion of their
reversibility problems has been solved. In this paper, we perform calculations
on two graphs and discover that the reversibility of any one-dimensional FCA
exhibits periodicity as the number of cells increases. We also successfully
provide a method to compute the reversibility sequence that encompasses the
reversibility of one-dimensional FCA with any number of cells. Additionally,
the calculations in this paper are applicable to FCA with various types of
boundaries. This means that we will have an efficient method to determine the
reversibility of almost all one-dimensional FCA, with a complexity independent
of cell number.
