Some properties of four-dimensional multicounter automata

Recently, due to the advances in many application areas such as computer animation, motion image processing, and so forth, it has become increasingly apparent that the study of four-dimensional pattern processing is of crucial importance. Thus, we think that research into four-dimensional automata as a computational model of four-dimensional pattern processing is also meaningful. This article introduces four-dimensional multicounter automata, and investigates some of their properties. We show the differences between the accepting powers of seven-way and eight-way four-dimensional multicounter automata, and between the accepting powers of deterministic and nondeterministic seven-way four-dimensional multicounter automata. This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2005