Embedding Arbitrary Boolean Circuits into Fungal Automata

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Abstract

Fungal automata are a variation of the two-dimensional sandpile automaton of Bak, Tang and Wiesenfeld (Phys. Rev. Lett., 1987). 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, 2021).

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Modanese, A., & Worsch, T. (2022). Embedding Arbitrary Boolean Circuits into Fungal Automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13568 LNCS, pp. 393–408). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20624-5_24

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