On Computational Hardness of Multidimensional Subtraction Games
We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is <b>EXP</b>-complete and requires time <inline-formula><math xmlns="http://www.w3...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-02-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/14/3/71 |
| Summary: | We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is <b>EXP</b>-complete and requires time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mrow><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></semantics></math></inline-formula>, where <i>n</i> is the input size. This bound is optimal up to a polynomial speed-up. The results are based on a construction introduced by Larsson and Wästlund. It relates subtraction games and cellular automata. |
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| ISSN: | 1999-4893 |