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
SN - 0304-3975
VL - 369
SP - 463
EP - 469
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 1-3
ER -