Optimal staged self-assembly of linear assemblies

Chalk, Cameron; Martinez, Eric; Schweller, Robert T.; Vega, Luis; Winslow, Andrew; Wylie, Tim

doi:10.1007/s11047-019-09740-y

Cited by 3 publications

(4 citation statements)

References 23 publications

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“…In the staged model, a constant-sized set of glue types is sufficient to build any shape by encoding the description in the mix graph. The trade-off between the number of glues, bins, and stages was further investigated in later work with 1 × n, O(1) × n [11], and general assemblies [10]. The complexity of verifying whether an assembly is uniquely produced is PSPACE-complete [6,15].…”

Section: Related Workmentioning

confidence: 99%

Simulation of Multiple Stages in Single Bin Active Tile Self-Assembly

Cirlos,

Gomez,

Grizzell

et al. 2023

Preprint

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Two significant and often competing goals within the field of self-assembly are minimizing tile types and minimizing human-mediated experimental operations. The introduction of the Staged Assembly and Single Staged Assembly models, while successful in the former aim, necessitate an increase in mixing operations later. In this paper, we investigate building optimal lines as a standard benchmark shape and building primitive.We show that a restricted version of the 1D Staged Assembly Model can be simulated by the 1D Freezing Tile Automata model with the added benefits of the complete automation of stages and completion in a single bin while maintaining bin parallelism and a competitive number of states for lines, patterned lines, and context-free grammars.

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Section: Related Workmentioning

confidence: 99%

Simulation of Multiple Stages in Single Bin Active Tile Self-Assembly

Cirlos,

Gomez,

Grizzell

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Related Workmentioning

confidence: 99%

“…Previous results show that both models have substantially increased power over the basic tile selfassembly models they generalize. In particular, by offloading some of the computation onto an experimenter responsible for performing the required mixing operations of the system between stages, SAM can build complex shapes and patterns in near-optimal complexity with respect to tile types, bin counts, and stage counts [10][11][12][13]20].…”

Section: Introductionmentioning

confidence: 99%

Simulation of Multiple Stages in Single Bin Active Tile Self-assembly

Cirlos

Gomez

Grizzell

et al. 2023

Lecture Notes in Computer Science

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Two significant and often competing goals within the field of self-assembly are minimizing tile types and minimizing human-mediated experimental operations. The introduction of the Staged Assembly and Single Staged Assembly models, while successful in the former aim, necessitate an increase in mixing operations later. In this paper, we investigate building optimal lines as a standard benchmark shape and building primitive. We show that a restricted version of the 1D Staged Assembly Model can be simulated by the 1D Freezing Tile Automata model with the added benefits of the complete automation of stages and completion in a single bin while maintaining bin parallelism and a competitive number of states for lines, patterned lines, and context-free grammars.

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“…This 2-handed tile selfassembly model [18,46] can also be used to let the subassemblies connect in phases, i.e., in a hierarchical manner [23]. One generalized version of hierarchical assembly is called "staged tile self-assembly" [19,20,24,26]. Instead of relying on square-shaped tiles, some generalizations are also already considered [25,29].…”

Section: Tile Self-assemblymentioning

confidence: 99%

Particle-Based Assembly Using Precise Global Control

et al. 2022

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In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is constructible. Previous work provides a class of shapes for which constructibility can be decided efficiently when particles move maximally into the same direction induced by a global signal. In this paper we consider the single step model, i.e., a model in which each particle moves one unit step into the given direction. We restrict the assembly process such that at each single time step actually one particle is added to and moved within the workspace. We prove that deciding constructibility is NP-complete for three-dimensional shapes, and that a maximum constructible shape can be approximated. The same approximation algorithm applies for 2D. We further present linear-time algorithms to decide whether or not a tree-shape in 2D or 3D is constructible. Scaling a shape yields constructibility; in particular we show that the 2-scaled copy of every non-degenerate polyomino is constructible. In the three-dimensional setting we show that the 3-scaled copy of every non-degenerate polycube is constructible.

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Optimal staged self-assembly of linear assemblies

Cited by 3 publications

References 23 publications

Simulation of Multiple Stages in Single Bin Active Tile Self-Assembly

Simulation of Multiple Stages in Single Bin Active Tile Self-Assembly

Simulation of Multiple Stages in Single Bin Active Tile Self-assembly

Particle-Based Assembly Using Precise Global Control

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