Modular Algorithm in Tile Self-assembly Model

  • Xiwen Fang
  • Xuejia Lai
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 237)

Abstract

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 .

Keywords

tile assembly model DNA computing modulus problem assembly time 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Xiwen Fang
    • 1
  • Xuejia Lai
    • 1
  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina

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