Bottom-up pyramid cellular acceptors with four-dimensional layers

摘要

In 1967, M. Blum and C. Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern processing. Since then, many researchers in this field have been investigating the many properties of two- or three-dimensional automata. In 1977, C.R. Dyer and A. Rosenfeld introduced an acceptor on a two-dimensional pattern (or tape) called the pyramid cellular acceptor, and demonstrated that many useful recognition tasks are executed by pyramid cellular acceptors in a time which is proportional to the logarithm of the diameter of the input. They also introduced a bottom-up pyramid cellular acceptor, which is a restricted version of the pyramid cellular acceptor, and proposed some interesting open problems about bottom-up pyramid cellular acceptors. On the other hand, we think that the study of four-dimensional automata has been meaningful as the computational model of four-dimensional information processing such as computer animation, moving picture processing, and so forth. In this article, we investigate bottom-up pyramid cellular acceptors with four-dimensional layers, and show some of their accepting powers.