Abstract
A morphogenetic system (M system) is an abstract computational model inspired by characteristic properties of morphogenetic phenomena such as controlled growth, self-reproduction, homeostasis and self-healing in living systems. Besides selected principles of membrane computing, M systems also rely on algorithmic self-assembly of abstract tiles unfolding in a 3D (or generally, dD) space. Explicit spatial arrangements for interaction among an M system’s components are crucial for its function. From a computational viewpoint, key features of M systems include their computational universality and their efficiency to solve difficult problems. Both computational universality (in the Turing sense) and self-healing properties (in the sense of the algorithmic tile assembly model) have been demonstrated for different M systems in prior publications. Here, we demonstrate that both of these properties can be simultaneously achieved in a single M system. We present a Turing universal string acceptor M system that also exhibits self-healing capabilities of degree 1. This result is rather surprising since Turing machines are usually very sensitive to minor damage to their internal structure. The result thus sheds light on the power and importance of geometric and spatial arrangements for the reliability and robustness of a computational system.
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Acknowledgements
This work was supported by The Ministry of Education, Youth and Sports Of the Czech Republic from the National Programme of Sustainability (NPU II) project IT4Innovations Excellence in Science - LQ1602, and by the Silesian University in Opava under the Student Funding Scheme, project SGS/11/2019.
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Sosík, P., Garzon, M. & Drastík, J. Self-healing turing-universal computation in morphogenetic systems. Nat Comput 20, 739–750 (2021). https://doi.org/10.1007/s11047-021-09860-4
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DOI: https://doi.org/10.1007/s11047-021-09860-4