REVERSIBILITY OF A SYMMETRIC LINEAR CELLULAR AUTOMATA.

The characterization of the size of the cellular space of a particular type of reversible symmetric linear cellular automata is introduced in this paper. Specifically, it is shown that those symmetric linear cellular with 2k + 1 cells, and whose transition matrix is a k-diagonal square band matrix with nonzero entries equal to 1 are reversible. Furthermore, in this case the inverse cellular automata are explicitly computed. Moreover, the reversibility condition is also studied for a general number of cells. [ABSTRACT FROM AUTHOR]