One of the most important research issues in the field of nanonetworks is the problem of constructing real networks in practice. To build such networks, one needs to create the nano-devices themselves as well as a computing and a communication mechanism. We already have developed such a concept based on DNA building blocks (so called DNA tiles), which is able to generate all three mechanisms by self-construction, basically by providing a sufficiently large number of specific DNA building blocks. Such networks are Turing complete; however, as we demonstrate in this paper, the number of required building blocks to execute computations by simulating Turing machines is large. We will show in this paper that the number can be reduced by using specific, more efficient sets of building blocks for problems that can be modeled as boolean formulas. For specific mathematical operations like And or Add, even smaller solutions/message molecules can be created.

This paper presents small message molecules for frequently requested mathematical problems. We present nanonetworks for the Thres and Add operations. Thres operations can be used to register if critical concentrations of disease markers have been reached. Add forms the basis for many advanced communication protocols. Furthermore, message molecules for Mult, Xor and Inc are conceptualized. The presented message molecules are smaller and less error prone compared to the tilesets that result from more generic approaches. It is therefore more likely that they can be employed in groundbreaking wet-lab experiments in the near future.

纳米网络领域最重要的研究问题之一是在实践中构建真实网络的问题。为了构建这样的网络，需要创建纳米设备本身以及计算和通信机制。我们已经开发出了一种基于DNA构建块（所谓的DNA拼贴）的概念，该概念基本上可以通过提供足够数量的特定DNA构建块来通过自我构建来生成所有三种机制。这样的网络是图灵完整的；但是，正如我们在本文中演示的那样，通过模拟图灵机执行计算所需的构件数量很多。我们将在本文中表明，可以通过使用特定的，更有效的构建模块集来减少问题的数量，这些问题可以建模为布尔公式。和或添加，可以创建更小的解决方案/消息分子。

本文介绍了一些经常遇到的数学问题的小信息分子。我们介绍了Thres和Add操作的纳米网络。Thres操作可用于记录是否已达到疾病标志物的临界浓度。添加表格是许多高级通信协议的基础。此外，对Mult，Xor和Inc的消息分子进行了概念化。与由更通用的方法产生的图块相比，所呈现的消息分子更小且更不易出错。因此，在不久的将来更有可能将其用于开创性的湿实验室实验中。