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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

Yiyang JIA

Seikei University

Jun MITANI

University of Tsukuba

Ryuhei UEHARA

JAIST

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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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},}

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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 -