ON CHARACTERIZATION OF STATE TRANSITION GRAPH OF ADDITIVE CELLULAR AUTOMATA BASED ON DEPTH

Characterization of additive cellular automata (CA) on the basis of the invariant, minimal and characteristic polynomials is reported in this paper. It is shown how a topological parameter, namely depth of the state transition graph of a CA, can be correlated with its characteristic polynomial. The approach is illustrated with reference to the analysis for four example CAs. Combinatorial treatment is formulated for these CAs and expressions are derived for the depth in relation to the number of cells in these CAs.