Remarks on Recognizability of Four-Dimensional Topological Components
Makoto Nagatomo, Makoto Sakamoto, Tatsuma Kurogi, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani, Takao Ito, Yasuo Uchida, Tsunehiro Yoshinaga · Journal of Robotics Networking and Artificial Life · 2014
The study of four-dimensional automata as the computational model of four-dimensional pattern processing has been meaningful.However, it is conjectured that the three-dimensional pattern processing has its our difficulties not arising in two-or three-dimensional case.One of these difficulties occurs in recognizing topological properties of four-dimensional patterns because the four-dimensional neighborhood is more complicated than two-or three-dimensional case.Generally speaking, a property or relationship is topological only if it is preserved when an arbitrary ' rubber-sheet ' distortion is applied to the pictures .For example, adjacency and connectedness are topological ; area, elongatedness, convexity, straightness, etc. are not.In recent years, there have been many interesting papers on digital topological properties.For example, an interlocking component was defined as a new topological property in multi-dimensional digital pictures, and it was proved that no one marker automaton can recognize interlocking components in a three-dimensional digital picture.In this paper, we deal with recognizability of topological components by four-dimensional Turing machines, and investigate some properties.