Powers and Limitations of Synchronous Self-Assembly
For researchers in algorithmic self-assembly, this work clarifies the fundamental power of synchronization and its limitations, revealing that the synchronous model enables constructions not possible asynchronously.
This paper demonstrates that synchronous self-assembly (syncTAM) is computationally more powerful than the asynchronous model (aTAM), particularly in the non-cooperative setting, by constructing assemblies impossible in aTAM such as a flagpole and a variant of the Sierpinski triangle. It also shows that limited synchronization with a threshold l is sensitive to the exact value of l, affecting simulation and shape formation.
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.