Remarks on Four-Dimensional Probabilistic Finite Automata

Abstract

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.

Some properties of ligkl/ig-neighborhood Template ligAl/ig-type two-dimensional bounded cellular acceptors

“…R' is one-neighborhood, so we can consider each cell of R' as usual one-dimensional finite automata. Then, each cell of R' moves to store all states that each corresponding cell of R can enter in each state at each time by using the well-known subset construction method (see (1) …”

“…An A-3DBCA(k) (A-3NBCA(k)) is called a k-neighborhood template A-type three-dimensional deterministic bounded cellular acceptor (k-neighborhood template A-type three-dimensional nondeterministic bounded cellular acceptor). This paper mainly investigates some open problems about accepting powers of A-3DBCA(k)'s whose configuration-readers are L(m) space-bounded deterministic (nondeterministic) three-dimensional Turing machines [1].…”

Remarks on Four-Dimensional Probabilistic Finite Automata

“…We next introduce a four-dimensional probabilistic finite automaton which is a natural extension of a three-dimensional probabilistic finite automaton to four dimension [25]. Let S be a finite set.…”

“…By the way, the question of whether processing fourdimensional digital patterns (three-dimensional digital patterns with time axis) such as computer animation, dynamic image processing, and so on is much difficult than two-or three-dimensional ones is of great interest from the theoretical and practical standpoints. From this point of view, we first proposed four-dimensional automata as computational models of four-dimensional pattern processing in 2002, and investigated their several accepting powers [21]. Since then, we have introduced several four-dimensional automata, and investigated their accepting powers and recognizability [22,24,26,27,32].…”

“…From this point of view, we first proposed four-dimensional automata as computational models of four-dimensional pattern processing in 2002, and investigated their several accepting powers [21]. Since then, we have introduced several four-dimensional automata, and investigated their accepting powers and recognizability [22,24,26,27,32]. On the other hand, the classes of sets recognized by two-or three-dimensional probabilistic finite automata and probabilistic Turing machines have been studied extensively [3-6, 9, 12-15, 17-19, 25, 28, 29, 33-35].…”