Multiplier System in the Tile Assembly Model with Reduced Tileset-Size
Previously a 28-tile multiplier system which computes the product of two numbers was proposed by Brun. However the tileset-size is not optimal. In this paper we prove that multiplication can be carried out using less tile types while maintaining the same time efficiency: we propose two new tile assembly systems, both can deterministically compute A*B for given A and B in constant time. Our first system requires 24 computational tile types while our second system requires 16 tile types, which achieve smaller constants than Brun’s 28-tile multiplier system.
Keywordstile assembly model DNA computing multiplier tileset-size
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