Chomp, Recurrences and Chaos(?)
2004; Taylor & Francis; Volume: 10; Issue: 13-15 Linguagem: Inglês
10.1080/10236190410001652720
ISSN1563-5120
Autores Tópico(s)Artificial Intelligence in Games
ResumoIn this article, dedicated with admiration and friendship to chaos and difference (and hence recurrence) equations guru Saber Elaydi, I give a new approach and a new algorithm for Chomp, David Gale's celebrated combinatorial game. This work is inspired by Xinyu Sun's "ultimate-periodicity" conjecture and by its brilliant proof by high-school student Steven Byrnes. The algorithm is implemented in a Maple package BYRNES accompanying this article. By looking at the output, and inspired by previous work of Andries Brouwer, I speculate that Chomp is chaotic, in a yet-to-be-made-precise sense, because the losing positions are given by "weird" recurrences.
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