Related papers: A pumping lemma for non-cooperative self-assembly
We consider non cooperative binding in so called `temperature 1', in deterministic (here called {\it confluent}) tile self-assembly systems (1-TAS) and prove the standing conjecture that such systems do not have universal computational…
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…
We investigate a fundamental question regarding a benchmark class of shapes in one of the simplest, yet most widely utilized abstract models of algorithmic tile self-assembly. Specifically, we study the directed tile complexity of a $k…
This paper concerns the self-assembly of scaled-up versions of arbitrary finite shapes. We work in the multiple temperature model that was introduced by Aggarwal, Cheng, Goldwasser, Kao, and Schweller (Complexities for Generalized Models of…
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model…
Winfree's abstract Tile Assembly Model (aTAM) is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing "seed" assembly based on specific binding sites on…
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…
In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which…
Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for an arbitrary finite, connected shape $X \subset \mathbb{Z}^2$, there is a tile set that uniquely self-assembles into a 3D representation of…
In this paper, we extend existing results about simulation and intrinsic universality in a model of tile-based self-assembly. Namely, we work within the 2-Handed Assembly Model (2HAM), which is a model of self-assembly in which assemblies…
As a mathematical model of self-assembling systems, Winfree's abstract Tile Assembly Model (aTAM) is a remarkable platform for studying the behaviors and powers of self-assembling systems. Capable of Turing universal computation, the aTAM…
The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal…
In the abstract Tile Assembly Model (aTAM) square tiles self-assemble, autonomously binding via glues on their edges, to form structures. Algorithmic aTAM systems can be designed in which the patterns of tile attachments are forced to…
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…
We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1…
We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…
The well-studied Two-Handed Tile Assembly Model (2HAM) is a model of tile assembly in which pairs of large assemblies can bind, or self-assemble, together. In order to bind, two assemblies must have matching glues that can simultaneously…
We introduce a new model of algorithmic tile self-assembly called size-dependent assembly. In previous models, supertiles are stable when the total strength of the bonds between any two halves exceeds some constant temperature. In this…
We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Of particular practical importance is to find tile…
We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et…