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.
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Montoya, J.A. (2012). Computing with Sand: On the Complexity of Recognizing Two-dimensional Sandpile Critical Configurations. In: Durand-Lose, J., Jonoska, N. (eds) Unconventional Computation and Natural Computation. UCNC 2012. Lecture Notes in Computer Science, vol 7445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32894-7_17
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DOI: https://doi.org/10.1007/978-3-642-32894-7_17
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