TY - JOUR

T1 - Crossing information in two-dimensional Sandpiles

AU - Gajardo, A.

AU - Goles, E.

N1 - Funding Information:
∗Corresponding author. E-mail addresses: anahi@ing-mat.udec.cl (A. Gajardo), eric.chacc@uai.cl (E. Goles). 1This work was partially supported by CONICYT FONDECYT #1030706, CONICYT FONDAP program in applied mathematics and by CNRS (E.G.).

PY - 2006/12/15

Y1 - 2006/12/15

N2 - We prove that in a two-dimensional Sandpile automaton, embedded in a regular infinite planar cellular space, it is impossible to cross information, if the bit of information is the presence (or absence) of an avalanche. This proves that it is impossible to embed arbitrary logical circuits in a Sandpile through quiescent configurations. Our result applies also for the non-planar neighborhood of Moore. Nevertheless, we also show that it is possible to compute logical circuits with a two-dimensional Sandpile, if a neighborhood of radius two is used in Z2; crossing information becomes possible in that case, and we conclude that for this neighborhood the Sandpile is P-complete and Turing universal.

AB - We prove that in a two-dimensional Sandpile automaton, embedded in a regular infinite planar cellular space, it is impossible to cross information, if the bit of information is the presence (or absence) of an avalanche. This proves that it is impossible to embed arbitrary logical circuits in a Sandpile through quiescent configurations. Our result applies also for the non-planar neighborhood of Moore. Nevertheless, we also show that it is possible to compute logical circuits with a two-dimensional Sandpile, if a neighborhood of radius two is used in Z2; crossing information becomes possible in that case, and we conclude that for this neighborhood the Sandpile is P-complete and Turing universal.

KW - Calculability

KW - Cellular automata

KW - Complexity

KW - Discrete dynamical system

KW - Sandpile

UR - http://www.scopus.com/inward/record.url?scp=33751212769&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2006.09.022

DO - 10.1016/j.tcs.2006.09.022

M3 - Article

AN - SCOPUS:33751212769

VL - 369

SP - 463

EP - 469

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-3

ER -