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In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla, Liu, and Seeman to…
The field of algorithmic self-assembly is concerned with the computational and expressive power of nanoscale self-assembling molecular systems. In the well-studied cooperative, or temperature 2, abstract tile assembly model it is known that…
We prove the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile Assembly Model, when restricted to…
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is…
Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must…
We prove a result which strongly hints at the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile…
In this paper we investigate the computational power of the polygonal tile assembly model (polygonal TAM) at temperature 1, i.e. in non-cooperative systems. The polygonal TAM is an extension of Winfree's abstract tile assembly model (aTAM)…
We prove a negative result on the power of a model of algorithmic self-assembly for which it has been notoriously difficult to find general techniques and results. Specifically, we prove that Winfree's abstract Tile Assembly Model, when…
We show the first asymptotically efficient constructions in the so-called "noncooperative planar tile assembly" model. Algorithmic self-assembly is the study of the local, distributed, asynchronous algorithms ran by molecules to…
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…
We prove that if a subset X of the integer Cartesian plane weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as *pumpability*, then X is a finite union of doubly…
We prove a Pumping Lemma for the noncooperative abstract Tile Assembly Model, a model central to the theory of algorithmic self-assembly since the beginning of the field. This theory suggests, and our result proves, that small differences…
Harnessing the intrinsic dynamics of physical systems for information processing opens new avenues for computation embodied in matter. Using simulations of a model system, we show that assemblies of DNA tiles capable of self-organizing into…
In the abstract Tile Assembly Model (aTAM), the phenomenon of cooperation occurs when the attachment of a new tile to a growing assembly requires it to bind to more than one tile already in the assembly. Often referred to as…
Is Winfree's abstract Tile Assembly Model (aTAM) "powerful?" Well, if certain tiles are required to "cooperate" in order to be able to bind to a growing tile assembly (a.k.a., temperature 2 self-assembly), then Turing universal computation…
Traditionally, computation within self-assembly models is hard to conceal because the self-assembly process generates a crystalline assembly whose computational history is inherently part of the structure itself. With no way to remove…
Self-assembly is a process which is ubiquitous in natural, especially biological systems. It occurs when groups of relatively simple components spontaneously combine to form more complex structures. While such systems have inspired a large…
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)…
We prove that if a set $X \subseteq \Z^2$ weakly self-assembles at temperature 1 in a deterministic tile assembly system satisfying a natural condition known as \emph{pumpability}, then $X$ is a finite union of semi-doubly periodic sets.…
We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we…