Computing with sand: on the complexity of recognizing two-dimensional sandpile critical configurations

Authors:
J. Andres Montoya
Affiliations:
Universidad Industrial de Santander, Bucaramanga, Colombia
Venue:
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Year:
2012

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Abstract

In this work we study the complexity of recognizing the critical configurations of The Two-dimensional Abelian Sandpile Model, we review some known facts and we prove that there does not exist a polylog-depth uniform polynomial size family of monotone boolean circuits solving this problem, this result suggests that the recognition of critical configurations cannot be accomplished in polylog time employing a polynomial number of processors.