Authors
Makoto Nagatomo, Makoto Sakamoto, Tatsuma Kurogi, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani, Takao Ito, Yasuo Uchida, Tsunehiro Yoshinaga
Corresponding Author
Makoto Sakamoto
Available Online 15 December 2014.
DOI
https://doi.org/10.2991/jrnal.2014.1.3.9How to use a DOI?
Keywords
digital geometry, interlocking component, one marker automaton, three-dimensional automaton, topological component, Turing machine
Abstract
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.

Copyright
© 2013, the Authors. Published by ALife Robotics Corp. Ltd..
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).