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Factoring Integers in the Tile Assembly Model

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Abstract:

Tile assembly model is a highly distributed parallel computation model. In this paper, three tile assembly model systems are proposed on the theoretical level, which can be combined together to factor integers in a nondeterministical way. The combined factoring tile system randomly produces one divisor, then performs division and at last, checks whether the remainder equals to zero. All these proposed tile systems complete computation in Θ(1) distinct tile types. Each assembly process is executed in parallel, producing the solution in linear time with respect to the size of the known dividend. To find the successful solutions among the many parallel final configuration assembled by DNA tiles, a "yes" tile is used as a mark. It is proved that the probability of such a nondeterministic tile assembly system succeeding to find the prime factor is closed to 1.

Keywords: DNA COMPUTATION; FACTORING SYSTEM; FUNCTION PACKAGE; IDENTIFIER TILES; NON-RESTORING DIVISION ALGORITHM; NONDETERMINISTIC COMPUTING; PARALLEL COMPUTING; SELF-ASSEMBLY; TILE ASSEMBLY MODEL

Document Type: Research Article

DOI: https://doi.org/10.1166/jctn.2010.1622

Publication date: 2010-11-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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