Advertisement

The Computational Complexity of One-Dimensional Sandpiles

  • Peter Bro Miltersen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

We prove that the one-dimensional sandpile prediction problem is in AC 1. The previously best known upper bound on the AC i -scale was AC 2. We also prove that it is not in AC 1 − − ε for any constant ε> 0.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of 1/f noise. Physical Review Letters 59, 381–384 (1987)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Physical Review A 38, 364–374 (1988)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Barrington, D.A.M., Immerman, N., Straubing, H.: On uniformity within NC 1. Journal of Computer and System Sciences 41(3), 274–306 Google Scholar
  4. 4.
    Chandra, A.K., Stockmeyer, L., Vishkin, U.: Constant depth reducibility. SIAM Journal on Computing 13, 423–439 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Griffeath, D., Moore, C.: Life without death is P-complete. Complex Systems 4, 299–318 (1990)MathSciNetGoogle Scholar
  6. 6.
    Håstad, J.: Computational Limitations of Small-Depth Circuits. ACM doctoral dissertation award 1986. MIT Press, Cambridge (1987)Google Scholar
  7. 7.
    Langton, C.G.: Computation at the edge of chaos. Physica D 42 (1990)Google Scholar
  8. 8.
    Machta, J.: The computational complexity of pattern formation. Journal of Statistical Physics 77, 755 (1994)zbMATHCrossRefGoogle Scholar
  9. 9.
    Machta, J., Greenlaw, R.: The computational complexity of generating random fractals. Journal of Statistical Physics 82, 1299 (1996)CrossRefGoogle Scholar
  10. 10.
    Moore, C., Nilsson, M.: The Computational Complexity of Sandpiles. Journal of Statistical Physics 96, 205–224 (1999), Also available on, http://www.santafe.edu/~moore/ zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Moore, C., Nordahl, M.G.: Predicting lattice gasses is P-complete. Santa Fe working Paper 97-04-034Google Scholar
  12. 12.
    Moore, C.: Majority-vote cellular automata, Ising dynamics, and P-completeness. Journal of Statistical Physics 88, 795–805 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Moriarty, K., Machta, J.: The computational complexity of the Lorentz lattices gas. Journal of Statistical Physics 87, 1245 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ruzzo, W.: Tree-size bounded alternation. Journal of Computer and Systems Sciences 21, 218–235 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sudborough, I.: On the tape complexity of deterministic context-free languages. Journal of the Association for Computing Machinery 25, 405–414 (1978)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter Bro Miltersen
    • 1
  1. 1.Dept. of Computer ScienceUniversity of AarhusDenmark

Personalised recommendations