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19 April 2024

» arxiv » 1607.1826

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Single-Player and Two-Player Buttons & Scissors Games
Kyle Burke ; Erik D. Demaine ; Harrison Gregg ; Robert A. Hearn ; Adam Hesterberg ; Michael Hoffmann ; Hiro Ito ; Irina Kostitsyna ; Jody Leonard ; Maarten Löffler ; Aaron Santiago ; Christiane Schmidt ; Ryuhei Uehara ; Yushi Uno ; Aaron Williams ;
Date:	7 Jul 2016
Abstract:	We study the computational complexity of the Buttons & Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for $C = 2$ colors but polytime solvable for $C = 1$. Similarly the game is NP-complete if every color is used by at most $F = 4$ buttons but polytime solvable for $F leq 3$. We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.
Source:	arXiv, 1607.1826
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