Turing-Completeness of Asynchronous Non-camouflage Cellular Automata
Asynchronous Boolean totalistic cellular automata have recently attracted attention as promising models for the implementation of reaction-diffusion systems. It is unknown, however, to what extent they are able to conduct computation. In this paper, we introduce the so-called non-camouflage property, which means that a cell’s update is insensitive to neighboring states that equal its own state. This property is stronger than the Boolean totalistic property, which signifies the existence of states in a cell’s neighborhood, but is not concerned with how many cells are in those states. We argue that the non-camouflage property is extremely useful for the implementation of reaction-diffusion systems, and we construct an asynchronous cellular automaton with this property that is Turing-complete. This indicates the feasibility of computation by reaction-diffusion systems.
KeywordsCellular Automaton Neighboring Cell Turing Machine Cell State Transition Rule
This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Robotics” (No. 15H00825 and No. 24104005) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan.
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