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Related papers: Parallelism and Time in Hierarchical Self-Assembly

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We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…

Computational Geometry · Computer Science 2014-11-26 Ho-Lin Chen , David Doty , Ján Maňuch , Arash Rafiey , Ladislav Stacho

Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…

Materials Science · Physics 2010-01-08 Rebecca Schulman , Erik Winfree

Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence…

Biological Physics · Physics 2025-03-14 Jeremy Guntoro , Thomas Ouldridge

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…

Computational Complexity · Computer Science 2020-02-11 Pierre-Étienne Meunier , Damien Regnault , Damien Woods

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.…

Computational Geometry · Computer Science 2024-05-13 Phillip Drake , Daniel Hader , Matthew J. Patitz

Majumder, Reif and Sahu have presented a stochastic model of reversible, error-permitting, two-dimensional tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time.…

Computational Complexity · Computer Science 2009-08-04 Aaron Sterling

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…

Formal Languages and Automata Theory · Computer Science 2022-11-28 Robert M. Alaniz , David Caballero , Sonya C. Cirlos , Timothy Gomez , Elise Grizzell , Andrew Rodriguez , Robert Schweller , Armando Tenorio , Tim Wylie

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…

Data Structures and Algorithms · Computer Science 2017-01-03 Erik D. Demaine , Sándor P. Fekete , Christian Scheffer , Arne Schmidt

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…

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.…

Emerging Technologies · Computer Science 2022-03-30 Andrew Alseth , Daniel Hader , Matthew J. Patitz

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 introduce the \emph{robust random number generation} problem where the goal is to design an abstract tile assembly system (aTAM system) whose terminal assemblies can be split into $n$ partitions such that a resulting…

Formal Languages and Automata Theory · Computer Science 2016-08-01 Cameron Chalk , Bin Fu , Eric Martinez , Robert Schweller , Tim Wylie

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…

Computational Geometry · Computer Science 2014-11-06 David Furcy , Samuel Micka , Scott M. Summers

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 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…

Computational Geometry · Computer Science 2008-03-04 Erik D. Demaine , Martin L. Demaine , Sandor P. Fekete , Mashhood Ishaque , Eynat Rafalin , Robert T. Schweller , Diane Souvaine

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…

Computational Geometry · Computer Science 2026-05-28 Florent Becker , Phillip Drake , Matthew J. Patitz , Ryder Smith

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

In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile…

Emerging Technologies · Computer Science 2022-04-05 Andrew Alseth , Jacob Hendricks , Matthew J. Patitz , Trent A. Rogers

An oritatami system (OS) is a theoretical model of self-assembly via co-transcriptional folding. It consists of a growing chain of beads which can form bonds with each other as they are transcribed. During the transcription process, the…

Data Structures and Algorithms · Computer Science 2018-07-16 Erik D. Demaine , Jacob Hendricks , Meagan Olsen , Matthew J. Patitz , Trent A. Rogers , Nicolas Schabanel , Shinnosuke Seki , Hadley Thomas

In this paper we consider a variant of population protocols in which agents are allowed to be connected by edges, known as the constructors model. During an interaction between two agents the relevant connecting edge can be formed,…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-01 Leszek Gasieniec , Paul Spirakis , Grzegorz Stachowiak