Characterization of three dimensional cellular automata over Z_m

In this work we study the algebraic behavior of three dimensional linear cellular automata over Z_m: we provide necessary and sufficient conditions for a three dimensional linear cellular automata over Z_m to be reversible or irreversible. As a consequence of our result we characterize three dimensional linear cellular automata under the null boundary conditions. Three dimensional cellular automata wasn't much studied by researches. Tsalides et al. characterized three dimensional cellular automata in [1] and then Hemmingsson investigated quasi periodic behavior of three dimensional cellular automata in [2].