A note on two-dimensional finite automata

Abstract

During the past about thirty-five years, many types of twoor three-dimensional automata have been proposed and investigated the properties of them as the computational model of pattern processing. On the other hand, recently, due to the advances in many application areas such as computer animation, motion image processing, and so on, the study of three-dimensional pattern processing with the time axis has been of crucial importance. Thus, we think that it is very useful for analyzing computation of three-dimensional pattern processing with the time axis to explicate the properties of four-dimensional automata. In this paper, we propose a four-dimensional Turing machine and a four-dimensional finite automaton, and show the space complexities necessary and sufficient for seven-way four-dimensional Turing machines to simulate four-dimensional finite automata, where each sidelength of each input tape of these automata is equivalent. Key-Words: Turing machine, finite automaton, on-line tessellation acceptor, four-dimensional input tape, determinism, nondeterminism, space-bound, configuration, computation, space complexity