连续空间中的自组装多边形瓦片计算
Computing in continuous space with self-assembling polygonal tiles
摘要：
在本文中，我们调查的计算能力的多边形瓷砖组装模型（多边形TAM）在温度1，即在非合作系统。多边形TAM是Winfree的抽象瓦片组装模型（aTAM）的扩展，它不仅允许正方形瓦片（如aTAM中），而且允许瓦片形状为多边形。虽然一些自组装的结果已经显示出在温度1的计算普适性，这些是第一个结果，这样做，从根本上依赖于瓷砖放置在连续的，而不是离散的，空间。利用aTAM的正方形瓦片，证明了温度为1的系统类在计算上不是普适的。在这里，我们表明，一类系统的瓦片是由一个正多边形P与n > 6边是计算通用的。另一方面，我们表明，系统的瓷砖由一个正多边形P与n <= 6不能计算使用任何已知的技术。此外，我们展示了一些类别的系统，其瓷砖组成的非正多边形与n >= 3边是计算上的普遍。
英文摘要：
In this paper we investigate the computational power of the polygonal tile assembly model (polygonal TAM) at temperature 1, i.e. in non-cooperative systems. The polygonal TAM is an extension of Winfree's abstract tile assembly model (aTAM) which not only allows for square tiles (as in the aTAM) but also allows for tile shapes that are polygons. Although a number of self-assembly results have shown computational universality at temperature 1, these are the first results to do so by fundamentally relying on tile placements in continuous, rather than discrete, space. With the square tiles of the aTAM, it is conjectured that the class of temperature 1 systems is not computationally universal. Here we show that the class of systems whose tiles are composed of a regular polygon P with n > 6 sides is computationally universal. On the other hand, we show that the class of systems whose tiles consist of a regular polygon P with n <= 6 cannot compute using any known techniques. In addition, we show a number of classes of systems whose tiles consist of a non-regular polygon with n >= 3 sides are computationally universal.
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