Universal Totalistic Asynchonous Cellular Automaton and Its Possible Implementation by DNA
This paper presents a Cellular Automaton (CA) model designed for possible implementation by the reaction and diffusion of DNA strands. The proposed CA works asynchronously, whereby each cell undergoes its transitions independently from other cells and at random times. The state of a cell changes in a cyclic manner, rather than according to an any-to-any mapping. The transition rules are designed as totalistic, i.e., the next state of a cell is determined only by the number of states in the neighborhood of the cell, not by their relative positions. Universal circuit elements are designed for the CA as well as wires and crossings to connect them, which implies that the CA is Turing-complete.
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