Advances in Symmetric Sandpiles

• Autorzy: Formenti E. , Masson B. , Pisokas T.
• Języki publikacji: EN

Abstrakty

EN

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed-point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains. Bounds for the transient length are also given.

Słowa kluczowe

EN

discrete dynamical system; SOC system; sandpiles; fixed point dynamics; transient length

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2007
• Tom: Vol. 76, nr 1-2
• Strony: 91--112
• Opis fizyczny: bibliogr. 12 poz., wykr.

Twórcy

autor

Formenti E.

autor

Masson B.

autor

Pisokas T.

• Laboratoire 13S, Universite de Nice-Sophia Antipolis, Bât. ESSI, 930 route des Colles, 06903 Sophia Antipolis Cedex, France,

Bibliografia

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• [4] Formenti, E., Masson, B.: A note on fixed points of generalized ice piles models, International Journal on Unconventional Computing, 2(2), 2006.
• [5] Formenti, E., Masson, B.: On computing fixed points for generalized sand piles, International Journal on Unconventional Computing, 2(1), 2006, 13-25.
• [6] Formenti, E.,Masson, B., Pisokas, T.: On symmetric sandpiles, Cellular Automata for Research and Industry (ACRI), 4173, Springer-Verlag, 2006.
• [7] Goles, E., Kiwi, M. A.: Games on line graphs and sandpile automata, Theoretical Computer Science, 115, 1993, 321-349.
• [8] Goles, E., Morvan, M., Phan, H. D.: Sandpiles and order structure of integer partitions, Discrete Applied Mathematics, 117(1-3), 2002, 51-64.
• [9] Goles, E., Morvan, M., Phan, H. D.: The structure of linear chip firing games and related models, Theoretical Computer Science, 270, 2002, 827-841.
• [10] Miltersen, P. B.: Two notes on the computational complexity of one-dimensional sandpiles, Technical Report RS-99-3, BRICS, 1999.
• [11] Moore, C., Nilsson, M.: The computational complexity of sandpiles, Journal of Statistical Physics, 96, 1999, 205-224.
• [12] Ruelle, P., Sen, S.: Toppling distributions in one-dimensional Abelian sandpiles, Journal of Physics A, 25, 1992, 1257-1264.