Recognizing the Repeatable Configurations of Time-Reversible Generalized Langton’s Ant Is PSPACE-Hard
Department of Information Science, Tokyo Denki University, Saitama 350-0394, Hatoyama, Japan
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Algorithms 2011, 4(1), 1-15; https://doi.org/10.3390/a4010001
Received: 21 December 2010 / Revised: 29 December 2010 / Accepted: 19 January 2011 / Published: 28 January 2011
Chris Langton proposed a model of an artificial life that he named “ant”: an agent- called ant- that is over a square of a grid moves by turning to the left (or right) accordingly to black (or white) color of the square where it is heading, and the square then reverses its color. Bunimovich and Troubetzkoy proved that an ant’s trajectory is always unbounded, or equivalently, there exists no repeatable configuration of the ant’s system. On the other hand, by introducing a new type of color where the ant goes straight ahead and the color never changes, repeatable configurations are known to exist. In this paper, we prove that determining whether a given finite configuration of generalized Langton’s ant is repeatable or not is PSPACE-hard. We also prove the PSPACE-hardness of the ant’s problem on a hexagonal grid.
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Keywords:
cellular automata; computational complexity; Langton’s ant; Lorentz lattice gas; PSPACE-hard
This is an open access article distributed under the Creative Commons Attribution License
MDPI and ACS Style
Tsukiji, T.; Hagiwara, T. Recognizing the Repeatable Configurations of Time-Reversible Generalized Langton’s Ant Is PSPACE-Hard. Algorithms 2011, 4, 1-15.
AMA Style
Tsukiji T, Hagiwara T. Recognizing the Repeatable Configurations of Time-Reversible Generalized Langton’s Ant Is PSPACE-Hard. Algorithms. 2011; 4(1):1-15.
Chicago/Turabian StyleTsukiji, Tatsuie; Hagiwara, Takeo. 2011. "Recognizing the Repeatable Configurations of Time-Reversible Generalized Langton’s Ant Is PSPACE-Hard" Algorithms 4, no. 1: 1-15.
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