Hierarchy Based on Configuration-Reader about k-Neighborhood Template A-Type Three-Dimensional Bounded Cellular Acceptor

Abstract

Blum and Hewitt first proposed two-dimensional automata as computational models of two-dimensional pattern processing-two-dimensional finite automata and marker automata, and investigated their pattern recognition abilities in 1967. Since then, many researchers in this field have investigated the properties of automata on two-or three-dimensional tapes. On the other hand, the question of whether or not processing four-dimensional digital patterns is more difficult than processing two-or three-dimensional ones is of great interest from both theoretical and practical standpoints. Thus, the study of four-dimensional automata as the computational models of four-dimensional pattern processing has been meaningful. From this point of view, we are interested in four-dimensional computational models, In this paper, we introduce a new four-dimensional computational model, k-neighborhood template A-type three-dimensional bounded cellular acceptor on four-dimensional input tapes, and investigate about hierarchy based on configuration-reader about this model.

Remarks on Four-Dimensional Probabilistic Finite Automata

“…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].…”