Journal of Robotics, Networking and Artificial Life

Volume 1, Issue 3, December 2014, Pages 212 - 215

Remarks on Recognizability of Four-Dimensional Topological Components

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.
Open Access
This is an open access article distributed under the CC BY-NC license.

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Journal
Journal of Robotics, Networking and Artificial Life
Volume-Issue
1 - 3
Pages
212 - 215
Publication Date
2014/12/15
ISSN (Online)
2352-6386
ISSN (Print)
2405-9021
DOI
https://doi.org/10.2991/jrnal.2014.1.3.9How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Makoto Nagatomo
AU  - Makoto Sakamoto
AU  - Tatsuma Kurogi
AU  - Satoshi Ikeda
AU  - Masahiro Yokomichi
AU  - Hiroshi Furutani
AU  - Takao Ito
AU  - Yasuo Uchida
AU  - Tsunehiro Yoshinaga
PY  - 2014
DA  - 2014/12/15
TI  - Remarks on Recognizability of Four-Dimensional Topological Components
JO  - Journal of Robotics, Networking and Artificial Life
SP  - 212
EP  - 215
VL  - 1
IS  - 3
SN  - 2352-6386
UR  - https://doi.org/10.2991/jrnal.2014.1.3.9
DO  - https://doi.org/10.2991/jrnal.2014.1.3.9
ID  - Nagatomo2014
ER  -