IEICE TRANSACTIONS on Fundamentals
Logical Matrix Representations in Map Folding
Summary :
Logical matrices are binary matrices often used to represent relations. In the map folding problem, each folded state corresponds to a unique partial order on the set of squares and thus could be described with a logical matrix. The logical matrix representation is powerful than graphs or other common representations considering its association with category theory and homology theory and its generalizability to solve other computational problems. On the application level, such representations allow us to recognize map folding intuitively. For example, we can give a precise mathematical description of a folding process using logical matrices so as to solve problems like how to represent the up-and-down relations between all the layers according to their adjacency in a flat-folded state, how to check self-penetration, and how to deduce a folding process from a given order of squares that is supposed to represent a folded state of the map in a mathematical and natural manner. In this paper, we give solutions to these problems and analyze their computational complexity.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.10 pp.1401-1412
- Publication Date
- 2022/10/01
- Publicized
- 2022/03/24
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAP1165
- Type of Manuscript
- PAPER
- Category
- Mathematical Systems Science
Authors
Yiyang JIA
Seikei University
Jun MITANI
University of Tsukuba
Ryuhei UEHARA
JAIST
Keyword
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Yiyang JIA, Jun MITANI, Ryuhei UEHARA, "Logical Matrix Representations in Map Folding" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 10, pp. 1401-1412, October 2022, doi: 10.1587/transfun.2021EAP1165.
Abstract: Logical matrices are binary matrices often used to represent relations. In the map folding problem, each folded state corresponds to a unique partial order on the set of squares and thus could be described with a logical matrix. The logical matrix representation is powerful than graphs or other common representations considering its association with category theory and homology theory and its generalizability to solve other computational problems. On the application level, such representations allow us to recognize map folding intuitively. For example, we can give a precise mathematical description of a folding process using logical matrices so as to solve problems like how to represent the up-and-down relations between all the layers according to their adjacency in a flat-folded state, how to check self-penetration, and how to deduce a folding process from a given order of squares that is supposed to represent a folded state of the map in a mathematical and natural manner. In this paper, we give solutions to these problems and analyze their computational complexity.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1165/_p
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@ARTICLE{e105-a_10_1401,
author={Yiyang JIA, Jun MITANI, Ryuhei UEHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Logical Matrix Representations in Map Folding},
year={2022},
volume={E105-A},
number={10},
pages={1401-1412},
abstract={Logical matrices are binary matrices often used to represent relations. In the map folding problem, each folded state corresponds to a unique partial order on the set of squares and thus could be described with a logical matrix. The logical matrix representation is powerful than graphs or other common representations considering its association with category theory and homology theory and its generalizability to solve other computational problems. On the application level, such representations allow us to recognize map folding intuitively. For example, we can give a precise mathematical description of a folding process using logical matrices so as to solve problems like how to represent the up-and-down relations between all the layers according to their adjacency in a flat-folded state, how to check self-penetration, and how to deduce a folding process from a given order of squares that is supposed to represent a folded state of the map in a mathematical and natural manner. In this paper, we give solutions to these problems and analyze their computational complexity.},
keywords={},
doi={10.1587/transfun.2021EAP1165},
ISSN={1745-1337},
month={October},}
Copy
TY - JOUR
TI - Logical Matrix Representations in Map Folding
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1401
EP - 1412
AU - Yiyang JIA
AU - Jun MITANI
AU - Ryuhei UEHARA
PY - 2022
DO - 10.1587/transfun.2021EAP1165
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2022
AB - Logical matrices are binary matrices often used to represent relations. In the map folding problem, each folded state corresponds to a unique partial order on the set of squares and thus could be described with a logical matrix. The logical matrix representation is powerful than graphs or other common representations considering its association with category theory and homology theory and its generalizability to solve other computational problems. On the application level, such representations allow us to recognize map folding intuitively. For example, we can give a precise mathematical description of a folding process using logical matrices so as to solve problems like how to represent the up-and-down relations between all the layers according to their adjacency in a flat-folded state, how to check self-penetration, and how to deduce a folding process from a given order of squares that is supposed to represent a folded state of the map in a mathematical and natural manner. In this paper, we give solutions to these problems and analyze their computational complexity.
ER -
English
