Related papers: Building Squares with Optimal State Complexity in …
In this paper, we work in a 2D version of the probabilistic variant of Winfree's abstract Tile Assembly Model defined by Chandran, Gopalkrishnan and Reif (SICOMP 2012) in which attaching tiles are sampled uniformly with replacement. First,…
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…
Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for all $N \in \mathbb{N}$, there is a tile set that uniquely self-assembles into an $N \times N$ square shape at temperature 1 with optimal…
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…
In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues.…
We study the role that parallelism plays in time complexity of Winfree's abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the "hierarchical" aTAM, two assemblies, both consisting of multiple tiles, are…
We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting ``nicely'' on a tree gives rise to a self-covering of a topological groupoid, and how the…
Working in Winfree's abstract tile assembly model, we show that a constant-size tile assembly system can be programmed through relative tile concentrations to build an n x n square with high probability, for any sufficiently large n. This…
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of…
Tile assembly systems in the abstract Tile Assembly Model (aTAM) are computationally universal and capable of building complex shapes, but DNA-based implementations encounter formidable error rates that stifle this theoretical potential.…
Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correction. We address both questions,…
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…
We analyze the number of tile types $t$, bins $b$, and stages necessary to assemble $n \times n$ squares and scaled shapes in the staged tile assembly model. For $n \times n$ squares, we prove $\mathcal{O}(\frac{\log{n} - tb - t\log t}{b^2}…
In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles…
We revisit constructions for distribution and synthesis of Zielonka's asynchronous automata in restricted settings. We show first a simple, quadratic, distribution construction for asynchronous automata, where the process architecture is…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
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…
The connection between self-assembly and computation suggests that a shape can be considered the output of a self-assembly ``program,'' a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest…
The 2-Handed Assembly Model (2HAM) is a tile-based self-assembly model in which, typically beginning from single tiles, arbitrarily large aggregations of static tiles combine in pairs to form structures. The Signal-passing Tile Assembly…