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 .
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References
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)
Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (1998)
Barish, R., Rothemund, P., Winfree, E.: Two computational primitives for algorithmic self-assembly: Copying and counting. Nano Letters 5(12), 2586–2592 (2005)
Rothemund, P., Papadakis, N., Winfree, E.: Algorithmic self-assembly of dna sierpinski triangles. PLoS Biology 2(12), e424 (2004)
Brun, Y.: Solving np-complete problems in the tile assembly model. Theoretical Computer Science 395(1), 31–46 (2008)
Brun, Y.: Improving efficiency of 3-SAT-solving tile systems. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 1–12. Springer, Heidelberg (2011)
Zhang, X., Wang, Y., Chen, Z., Xu, J., Cui, G.: Arithmetic computation using self-assembly of dna tiles: subtraction and division. Progress in Natural Science 19(3), 377–388 (2009)
Winfree, E., Liu, F., Wenzler, L., Seeman, N., et al.: Design and self-assembly of two-dimensional dna crystals. Nature 394(6693), 539–544 (1998)
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Fang, X., Lai, X. (2014). Modular Algorithm in Tile Self-assembly Model. In: Abraham, A., Krömer, P., Snášel, V. (eds) Innovations in Bio-inspired Computing and Applications. Advances in Intelligent Systems and Computing, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-01781-5_13
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DOI: https://doi.org/10.1007/978-3-319-01781-5_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01780-8
Online ISBN: 978-3-319-01781-5
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