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Morphogenetic computing: computability and complexity results

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Abstract

A morphogenetic (M) system is an abstract computational model combining properties of membrane (P) systems, such as computing via abstract particles in separate compartments regulating their workflow, with algorithmic self-assembly generalizing original Wang tiles to arbitrary polytopes forming complex shapes in 2D/3D (or generally, dD) space. Even very simple morphogenetic systems can exhibit complex self-organizing behaviour and, at the abstract level, one can observe characteristic properties of morphogenetic phenomena such as controlled growth, self-reproduction, homeostasis and self-healing. Here we focus on computational aspects of the morphogenetic systems. After summarizing a series of results related to their computational universality (in the Turing sense) and computational complexity, we present two small universal M systems (one of them self-healing) and we also demonstrate how morphogenetic systems relate to the classes P and NP.

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Acknowledgements

This work was supported by the Silesian University in Opava under the Student Funding Scheme, project SGS/8/2022.

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  1. Faculty of Philosophy and Science, Institute of Computer Science, Silesian University in Opava, Opava, Czech Republic

    Petr Sosík

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  1. Petr Sosík
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Correspondence to Petr Sosík.

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Sosík, P. Morphogenetic computing: computability and complexity results. Nat Comput 22, 161–170 (2023). https://doi.org/10.1007/s11047-022-09899-x

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