Remarks on Four-Dimensional Probabilistic Finite Automata

This paper is a study of four-dimensional automata. Recently, due to the advances in many application areas such as dynamic image processing, computer animation, augmented reality (AR), and so on, it is useful for analyzing computation of four-dimensional information processing (three-dimensional pattern processing with time axis) to explicate the properties of four-dimensional automata. From this point of view, we have investigated many properties of four-dimensional automata and computational complexity. On the other hand, the class of sets accepted by probabilistic machines have been studied extensively. As far as we know, however, there is no results concerned with four-dimensional probabilistic machines. In this paper, we introduce four-dimensional probabilistic finite automata, and investigate some accepting powers of them.