自组装程序设计的内存一致性条件
Memory Consistency Conditions for Self-Assembly Programming
摘要：
也许关于自组装代理程序设计的两个最重要的理论问题是：（1）产生唯一终端组件的必要和充分条件，以及（2）错误校正。我们解决这两个问题，通过减少两个良好的研究模型的瓷砖组装模型的分布式共享内存（DSM），以获得结果的内存一致性系统诱导瓷砖组装系统时，在DSM设置模拟。抽象瓦片组装模型（aTAM）可以由服从因果一致性的DSM系统来模拟，aTAM中的局部确定性瓦片组装系统正好对应于在这样的模型中模拟瓦片组装的无并发写程序。因此，检测本地确定性的失败（这以前是一个开放的问题）减少到检测模拟程序中的数据竞争。此外，动力学瓦片组装模型可以由遵循GWO的DSM系统来模拟，GWO是由Steinke和Nutt定义的存储器一致性条件。(To我们的知识，这是DSM系统服从GWO的第一个自然例子，但没有更强的一致性条件。我们结合这些结果的观察，自组装算法是本地算法，并存在一个快速转换的确定性本地算法到确定性的自稳定算法。这提供了Soloveichik等人关于存在同时执行两种形式的自稳定的瓦片组装系统的定理的“立即”推广：校对和自修复。我们的简化和证明技术可以扩展到各种介质中的自组装代理程序，而不仅仅是DNA瓦片，也不仅仅是二维表面。
英文摘要：
Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correction. We address both questions, by reducing two well-studied models of tile assembly to models of distributed shared memory (DSM), in order to obtain results from the memory consistency systems induced by tile assembly systems when simulated in the DSM setting. The Abstract Tile Assembly Model (aTAM) can be simulated by a DSM system that obeys causal consistency, and the locally deterministic tile assembly systems in the aTAM correspond exactly to the concurrent-write free programs that simulate tile assembly in such a model. Thus, the detection of the failure of local determinism (which had formerly been an open problem) reduces to the detection of data races in simulating programs. Further, the Kinetic Tile Assembly Model can be simulated by a DSM system that obeys GWO, a memory consistency condition defined by Steinke and Nutt. (To our knowledge, this is the first natural example of a DSM system that obeys GWO, but no stronger consistency condition.) We combine these results with the observation that self-assembly algorithms are local algorithms, and there exists a fast conversion of deterministic local algorithms into deterministic self-stabilizing algorithms. This provides an "immediate" generalization of a theorem by Soloveichik et al. about the existence of tile assembly systems that simultaneously perform two forms of self-stabilization: proofreading and self-healing. Our reductions and proof techniques can be extended to the programming of self-assembling agents in a variety of media, not just DNA tiles, and not just two-dimensional surfaces.
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