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Algorithms
Volume 14
Issue 3
10.3390/a14030070
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Article

EXPTIME Hardness of an n by n Custodian Capture Game

by
Fumitaka Ito
1,†,‡,
Masahiko Naito
1,‡,
Naoyuki Katabami
1,‡ and
Tatsuie Tsukiji
2,*
1
Department of Science and Engineering, Tokyo Denki University, Tokyo 120-8551, Japan
2
Graduate School of Advanced Science and Technology, Tokyo Denki University, Tokyo 120-8551, Japan
*
Author to whom correspondence should be addressed.
†
Current address: Oaza Ishizuka, Hikigun Hatoyama-tyou, Saitama 350-0394, Japan.
‡
These authors contributed equally to this work.
Algorithms 2021, 14(3), 70; https://doi.org/10.3390/a14030070
Submission received: 26 January 2021 / Revised: 14 February 2021 / Accepted: 18 February 2021 / Published: 24 February 2021
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Abstract

Custodian capture occurs when a player has placed two of his pieces on the opposite sides of an orthogonal line of the opponent’s men. Each piece moves like the rook in Chess. Different cultures played it from pre-modern times in two-player strategy board games, Ludus Latrunculorum (Kowalski’s reconstruction), Hasami shogi in Japan, Mak-yek in Thailand and Myanmar, Ming Mang in Tibet, and so on. We prove that a custodian capture game on n×n square board is EXPTIME hard if the first player to capture five or more men in total wins.
Keywords: computational complexity; custodial capture; EXPTIME hard; generalized game; repetition computational complexity; custodial capture; EXPTIME hard; generalized game; repetition

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MDPI and ACS Style

Ito, F.; Naito, M.; Katabami, N.; Tsukiji, T. EXPTIME Hardness of an n by n Custodian Capture Game. Algorithms 2021, 14, 70. https://doi.org/10.3390/a14030070

AMA Style

Ito F, Naito M, Katabami N, Tsukiji T. EXPTIME Hardness of an n by n Custodian Capture Game. Algorithms. 2021; 14(3):70. https://doi.org/10.3390/a14030070

Chicago/Turabian Style

Ito, Fumitaka, Masahiko Naito, Naoyuki Katabami, and Tatsuie Tsukiji. 2021. "EXPTIME Hardness of an n by n Custodian Capture Game" Algorithms 14, no. 3: 70. https://doi.org/10.3390/a14030070

APA Style

Ito, F., Naito, M., Katabami, N., & Tsukiji, T. (2021). EXPTIME Hardness of an n by n Custodian Capture Game. Algorithms, 14(3), 70. https://doi.org/10.3390/a14030070

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