Exploring Cycle Structures of Additive Cellular Automata

This paper reports the complete characterization of additive cellular automaton (ACA) that employs xor and xnor logic to realize its next state function. Compared to linear cellular automaton (LCA) [3], which employs only xor logic in its next state function, an ACA displays much more wider varieties of state transition behavior leading to enhanced computing power. An analytical framework is developed to characterize the cyclic vector subspaces of an ACA that can be derived from careful analysis of the vector subspaces covered by the LCA. A scheme is proposed to explore the ACA structures having different state transition behavior than that of its LCA counterpart. The reported theoretical analysis justifies the nature of differences.