Embedding Arbitrary Boolean Circuits into Fungal Automata

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 ho...

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Veröffentlicht in:Algorithmica 2024, Vol.86 (7), p.2069-2091
Hauptverfasser: Modanese, Augusto, Worsch, Thomas
Format: Artikel
Sprache:eng
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Zusammenfassung: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 ( log B ) 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 ).
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-024-01222-7