基于Adleman-Lipton模型的快速矩阵乘法技术
Fast matrix multiplication techniques based on the Adleman-Lipton model
摘要：
在分布式存储器电子计算机上，快速并行矩阵乘法算法的实现和关联已经产生了惊人的结果和见解。在这篇论文中，我们使用分子生物学的工具来证明Strassen的快速矩阵乘法算法与DNA的理论编码的基础上的$n$ -模集的剩余数系统，从而证明计算数学与DNA的可行性。其结果是，一般可扩展的实现该模型的DNA计算范式，并可以推广到DNA计算机上的应用程序的\emph{all}快速矩阵乘法算法。我们还讨论了这种可扩展的实现的实际能力和问题。用DNA进行矩阵计算的快速方法很重要，因为它们也允许用DNA有效地实现其他算法（即求逆、计算行列式和图论）。
英文摘要：
On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen's fast matrix multiplication algorithm with DNA based on an $n$-moduli set in the residue number system, thereby demonstrating the viability of computational mathematics with DNA. As a result, a general scalable implementation of this model in the DNA computing paradigm is presented and can be generalized to the application of \emph{all} fast matrix multiplication algorithms on a DNA computer. We also discuss the practical capabilities and issues of this scalable implementation. Fast methods of matrix computations with DNA are important because they also allow for the efficient implementation of other algorithms (i.e. inversion, computing determinants, and graph theory) with DNA.
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