Abstract
In this work we study the complexity of the three-dimensional sandpile avalanches triggered by the addition of two critical configurations. We prove that the algorithmic problem consisting in predicting the evolution of three dimensional critical avalanches is the hardness core of the three-dimensional Abelian Sandpile Model. On the other hand we prove that three-dimensional critical avalanches are superlinear long on average. It suggests that the prediction problem is superlinear-hard on average.
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References
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized Criticality. Physical Review A 38, 364–374 (1988)
Dhar, D.: Theoretical Studies of Self-organized Criticality. Physica A 369, 29–70 (2006)
Mejía, C., Montoya, A.: On the Algorithmic Complexity of the Abelian Sandpile Model. In: Proceedings of Automata 2009, pp. 147–162 (2009) (submitted)
Moore, C., Nilsson, M.: The computational complexity of sandpiles. Journal of Statistical Physics 96, 205–224 (1999)
Tardos, G.: Polynomial bound for a chip firing game on graphs. SIAM J. Discrete Mathematics 1, 397–398 (1988)
Toumpakari, E.: On the abelian sandpile model. Ph.D. Thesis, University of Chicago (2005)
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Mejía, C., Andrés Montoya, J. (2010). The Complexity of Three-Dimensional Critical Avalanches. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds) Cellular Automata. ACRI 2010. Lecture Notes in Computer Science, vol 6350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15979-4_17
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DOI: https://doi.org/10.1007/978-3-642-15979-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15978-7
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