In abstract models of algorithmic self-assembly, synchronization between attachments has emerged as a crucial distinction between the classical asynchronous model (aTAM) and a new synchronous model, the syncTAM. This paper presents recent advances in gauging the additional power afforded by the syncTAM. While it is known that the syncTAM and the aTAM are each unable to fully simulate the other, this paper offers evidence that the syncTAM is computationally significantly more powerful than the aTAM, especially in the non-cooperative setting. The additional power of the non-cooperative syncTAM is witnessed by the following constructions, all impossible in the non-cooperative aTAM: a flagpole, a strict self-assembly of a variant of the discrete Sierpinski triangle, and the ability to build the same assemblies (modulo scale factor) as directed aTAM systems. The second topic is that of limited synchronization, wherein, when the number of attachments is smaller than some threshold $l$, they happen synchronously, but attachments in excess of that number must wait. In that context, the precise value of $l$ is crucial, and changes to that value prevent simulation and can change which shapes can be obtained.

翻译：在算法自组装的抽象模型中，附着过程之间的同步已成为经典异步模型（aTAM）与新型同步模型（syncTAM）之间的关键区别。本文展示了评估syncTAM所赋予额外能力的最新进展。尽管已知syncTAM与aTAM均无法完全模拟对方，但本文提供了证据表明，syncTAM在计算能力上显著强于aTAM，尤其是在非协作环境中。非协作syncTAM的额外能力体现在以下构造中——这些在非协作aTAM中均无法实现：旗杆结构、离散谢尔宾斯基三角形变体的严格自组装，以及构建与有向aTAM系统相同组装体（模尺度因子）的能力。第二个主题是有限同步，即当附着数量小于某个阈值$l$时，这些附着同步发生，但超出该数量的附着必须等待。在此情境下，$l$的精确取值至关重要，其变化不仅会阻止模拟，还会改变可获得的形状集合。