March 2024
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15 Reads
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1 Citation
Algorithmica
Fungal automata are a variation of the two-dimensional sandpile automaton of Bak et al. (Phys Rev Lett 59(4):381–384, 1987. https://doi.org/10.1103/PhysRevLett.59.381). In each step toppling cells emit grains only to some of their neighbors chosen according to a specific update sequence. We show how to embed any Boolean circuit into the initial configuration of a fungal automaton with update sequence HV. In particular we give a constructor that, given the description B of a circuit, computes the states of all cells in the finite support of the embedding configuration in O(logB) space. As a consequence the prediction problem for fungal automata with update sequence HV is P-complete. This solves an open problem of Goles et al. (Phys Lett A 384(22):126541, 2020. https://doi.org/10.1016/j.physleta.2020.126541).