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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)…

Emerging Technologies · Computer Science 2019-06-06 John Calvin Alumbaugh , Joshua J. Daymude , Erik D. Demaine , Matthew J. Patitz , Andrea W. Richa

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…

Computational Geometry · Computer Science 2014-04-30 Andrew Winslow

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…

Computational Complexity · Computer Science 2015-07-31 Pierre-Étienne Meunier , Damien Regnault

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,…

Data Structures and Algorithms · Computer Science 2024-08-13 David Furcy , Scott M. Summers

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…

Computational Geometry · Computer Science 2015-03-17 Jacob Hendricks , Matthew J. Patitz , Trent A. Rogers

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…

Computational Complexity · Computer Science 2016-10-28 Pierre-Étienne Meunier , Damien Regnault

Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…

Emerging Technologies · Computer Science 2012-07-06 Abhishek Chhajer , Manish K. Gupta , Sandeep Vasani , Jaley Dholakiya

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…

We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are…

Discrete Mathematics · Computer Science 2023-06-19 Florent Becker , Shahrzad Heydarshahi

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…

Emerging Technologies · Computer Science 2013-12-16 Tyler Fochtman , Jacob Hendricks , Jennifer E. Padilla , Matthew J. Patitz , Trent A. Rogers

We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no…

Computational Complexity · Computer Science 2015-03-13 Matthew Cook , Yunhui Fu , Robert T. Schweller

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…

Computational Geometry · Computer Science 2014-08-22 Erik D. Demaine , Matthew J. Patitz , Trent A. Rogers , Robert T. Schweller , Scott M. Summers , Damien Woods

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…

Computational Complexity · Computer Science 2021-07-19 Pierre-Etienne Meunier , Damien Regnault

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar…

Computational Geometry · Computer Science 2014-07-11 Pierre-Étienne Meunier

A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…

Statistical Mechanics · Physics 2017-02-27 Stephen Whitelam

In this paper we consider the time complexity of computing the sum and product of two $n$-bit numbers within the tile self-assembly model. The (abstract) tile assembly model is a mathematical model of self-assembly in which system…

Data Structures and Algorithms · Computer Science 2013-08-06 Alexandra Keenan , Robert Schweller , Michael Sherman , Xingsi Zhong

DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile…

Data Structures and Algorithms · Computer Science 2012-10-23 Ho-Lin Chen , Ming-Yang Kao

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…

Computational Geometry · Computer Science 2016-08-18 Austin Luchsinger , Robert Schweller , Tim Wylie

In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding…

Formal Languages and Automata Theory · Computer Science 2022-06-09 Andrew Alseth , Daniel Hader , Matthew J. Patitz

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…

Computational Complexity · Computer Science 2008-06-22 David Soloveichik , Erik Winfree