Modular Algorithm in Tile Self-assembly Model
In this paper we propose a system computing A mod B for given n A -bit binary integer A and n B -bit binary integer B, which is the first system directly solving the modulus problem in tile assembly model. The worst-case assembly time of our system is Θ(n A (n A − n B )) and the best-case assembly time is Θ(n A ).
Although the pre-existing division system which computes A/B can also be used to compute A mod B, the assembly time of this system is not ideal in some cases. Compared with the pre-existing division system, we achieved improved time complexity in our system. Our advantage is more significant if n A is much greater than n B .
Keywordstile assembly model DNA computing modulus problem assembly time
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- 1.Rothemund, P., Winfree, E.: The program-size complexity of self-assembled squares. In: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 459–468. ACM (2000)Google Scholar
- 2.Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (1998)Google Scholar
- 4.Rothemund, P., Papadakis, N., Winfree, E.: Algorithmic self-assembly of dna sierpinski triangles. PLoS Biology 2(12), e424 (2004)Google Scholar