An Approach to Constructing and Simulating Block Cellular Automata by Gellular Automata

Abstract

The model of gellular automata (GA) was proposed as one of the computational models based on DNA chemical reactions. GA consists of cells filled with solutions, where molecular reactions including DNA strand displacement reactions take place. Some of the products of the reactions act like keys, which may open or close the cells' walls since the walls consist of DNAbased gels and can be triggered to open or close by predefined DNA strands. While a wall between cells is open, the solutions of those cells mix with each other and it may arise new reactions.Thus we can control the "signal exchange" between neighbor cells. Although GA was shown to be computationally universal in our previous study, the power of parallel computation of GA was not utilized. To demonstrate the power, we show a general method to construct gellular automata that simulate arbitrary block cellular automata (block CA) with Margolus neighborhoods.