Extending DNA-Sticker Arithmetic to Arbitrary Size Using Staples

The simple-sticker model uses robotic processing of DNA strands contained in a fixed number of tubes to implement massively-parallel processing of bit strings. The bits whose value are '1' are recorded by short DNA "stickers" that hybridize at specific places on the strand. Other DNA models, like folded origami, use "staples" that hybridize to disjoint portions of a single strand. This paper proposes an extended-sticker paradigm that uses staples to hybridize to contiguous portions of two substrands, forming virtual strands. The problem of redundant bits is solved by blotting out old values. As an example of the novel extended-sticker paradigm, a log-time summation algorithm outperforms with an ideal implementation any electronic supercomputer conceivable in the near future for large data sets. JavaScript and CUDA simulations validate the theoretical operation of the proposed algorithm.