Matthew J. Patitz

Florent Becker, Phillip Drake, Matthew J. Patitz et al.

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.

John Calvin Alumbaugh, Joshua J. Daymude, Erik D. Demaine et al.

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA) model was recently introduced as a platform to help study connections between various models of self-assembly. However, in this paper we present a result in which we use TA to simulate arbitrary systems within the amoebot model, a theoretical model of programmable matter in which the individual components are relatively simple state machines that are able to sense the states of their neighbors and to move via series of expansions and contractions. We show that for every amoebot system, there is a TA system capable of simulating the local information transmission built into amoebot particles, and that the TA "macrotiles" used to simulate its particles are capable of simulating movement (via attachment and detachment operations) while maintaining the necessary properties of amoebot particle systems. The TA systems are able to utilize only the local interactions of state changes and binding and unbinding along tile edges, but are able to fully simulate the dynamics of these programmable matter systems.