International Workshop on Cellular Automata and Discrete Complex Systems

AUTOMATA 2014: Cellular Automata and Discrete Complex Systems pp 21-30 | Cite as

Computational Complexity of the Avalanche Problem on One Dimensional Kadanoff Sandpiles

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8996)


In this paper we prove that the general avalanche problemAP is in NC  for the Kadanoff sandpile model in one dimension, answering an open problem of [2]. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).


Sandpile models Discrete dynamical systems Computational complexity Dimension sensitive problems 


  1. 1.
    Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Formenti, E., Goles, E., Martin, B.: Computational complexity of avalanches in the kadanoff sandpile model. Fundam. Inform. 115(1), 107–124 (2012)MathSciNetMATHGoogle Scholar
  3. 3.
    Formenti, E., Masson, B.: On computing fixed points for generalized sand piles. Int. J. on Unconventional Comput. 2(1), 13–25 (2005)Google Scholar
  4. 4.
    Formenti, E., Masson, B., Pisokas, T.: Advances in symmetric sandpiles. Fundam. Inform. 76(1–2), 91–112 (2007)MathSciNetMATHGoogle Scholar
  5. 5.
    Formenti, E., Van Pham, T., Phan, H.D., Tran, T.H.: Fixed point forms of the parallel symmetric sandpile model. Theor. Comput. Sci. 322(2), 383–407 (2014)MathSciNetMATHGoogle Scholar
  6. 6.
    Gajardo, A., Goles, E.: Crossing information in two-dimensional sandpiles. Theor. Comput. Sci. 369(1–3), 463–469 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Goles, E., Margenstern, M.: Sand pile as a universal computer. Int. J. Mod. Phys. C 7(2), 113–122 (1996)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Goles, E., Morvan, M., Phan, H.D.: The structure of a linear chip firing game and related models. Theor. Comput. Sci. 270(1–2), 827–841 (2002)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Laredo, J.L.J., Bouvry, P., Guinand, F., Dorronsoro, B., Fernandes, C.: The sandpile scheduler. Cluster Comput. 17(2), 191–204 (2014)CrossRefGoogle Scholar
  10. 10.
    Perrot, K., Phan, H.D., Van Pham, T.: On the set of fixed points of the parallel symmetric sand pile model. Full Pap. AUTOMATA 2011, 17–28 (2011)MATHGoogle Scholar
  11. 11.
    Perrot, K., Rémila, E.: Avalanche structure in the kadanoff sand pile model. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 427–439. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  12. 12.
    Perrot, K., Rémila, E.: Transduction on kadanoff sand pile model avalanches, application to wave pattern emergence. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 508–519. Springer, Heidelberg (2011) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Enrico Formenti
    • 1
  • Kévin Perrot
    • 1
    • 2
    • 3
  • Éric Rémila
    • 4
  1. 1.Laboratoire I3S (UMR 6070 - CNRS)Université Nice Sophia AntipolisSophia Antipolis CedexFrance
  2. 2.Université de Lyon - LIP (UMR 5668 - CNRS - ENS de Lyon - Université Lyon 1)Lyon Cedex 7France
  3. 3.Universidad de Chile - DII - DIM - CMM (UMR 2807 - CNRS)SantiagoChile
  4. 4.Université de Lyon - GATE LSE (UMR 5824 - CNRS - Université Lyon 2)Saint-etienne Cedex 2France

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