Universal shape replication via self-assembly with signal-passing tiles

IF 1.7 4区 计算机科学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Natural Computing Pub Date : 2024-04-27 DOI:10.1007/s11047-024-09987-0
Andrew Alseth, Daniel Hader, Matthew J. Patitz
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Abstract

In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of other glues via “signals”. Specifically, the problem we investigate is “shape replication” wherein, given a set of input assemblies of arbitrary shape, a system must construct an arbitrary number of assemblies with the same shapes and, with the exception of size-bounded junk assemblies that result from the process, no others. We provide the first fully universal shape replication result, namely a single tile set capable of performing shape replication on arbitrary sets of any 3-dimensional shapes without requiring any scaling or pre-encoded information in the input assemblies. Our result requires the input assemblies to be composed of signal-passing tiles whose glues can be deactivated to allow deconstruction of those assemblies, which we also prove is necessary by showing that there are shapes whose geometry cannot be replicated without deconstruction. Additionally, we modularize our construction to create systems capable of creating binary encodings of arbitrary shapes, and building arbitrary shapes from their encodings. Because the STAM is capable of universal computation, this then allows for arbitrary programs to be run within an STAM system, using the shape encodings as input, so that any computable transformation can be performed on the shapes. This is the full version, containing all construction and proof details, of a previously published extended abstract version that had most details omitted.

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通过信号传递瓦片自组装实现通用形状复制
在本文中,我们研究了一种基于瓦片的自组装模型--信号传递瓦片组装模型(STAM)--的形状组装能力。在该模型中,通过 "信号",其他粘合剂的粘合作用可以开启或关闭将瓷砖粘合在一起的粘合剂。具体来说,我们研究的问题是 "形状复制",即在给定一组任意形状的输入装配体的情况下,系统必须构建任意数量的具有相同形状的装配体,除了在此过程中产生的有尺寸限制的垃圾装配体之外,不能有其他装配体。我们提供了第一个完全通用的形状复制结果,即单个瓦片集能够在任意三维形状的任意集合上执行形状复制,而不需要输入集合中的任何缩放或预编码信息。我们的结果要求输入组件由信号传递瓦片组成,这些瓦片的粘合剂可以停用,以允许解构这些组件,我们还通过证明有些形状的几何形状在不解构的情况下无法复制,证明了这一点的必要性。此外,我们还将我们的构造模块化,以创建能够为任意形状创建二进制编码的系统,并根据编码构建任意形状。由于 STAM 能够进行通用计算,因此可以在 STAM 系统中运行任意程序,将形状编码作为输入,这样就可以在形状上执行任何可计算的变换。本文是完整版,包含所有构造和证明细节,而之前发表的扩展摘要版省略了大部分细节。
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来源期刊
Natural Computing
Natural Computing Computer Science-Computer Science Applications
CiteScore
4.40
自引率
4.80%
发文量
49
审稿时长
3 months
期刊介绍: The journal is soliciting papers on all aspects of natural computing. Because of the interdisciplinary character of the journal a special effort will be made to solicit survey, review, and tutorial papers which would make research trends in a given subarea more accessible to the broad audience of the journal.
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