ASARG Github is active

For the past few years, our large software projects have lived in github under different personal accounts. We have finally set up ASARG as an organization and all our projects live together. For an overview, see the Software page. The github page is here: https://github.com/asarg/.

Adding pages

We’re just now getting around to updating the website with many of the projects we have going on. A software page has been added that we we begin outlining some of the simulators we have that are open source and publicly available.

Optimal Staged Self-Assembly of Linear Assemblies

Title: Optimal Staged Self-Assembly of Linear Assemblies
Authors: Cameron Chalk, Eric Martinez, Robert Schweller, Luis Vega, Andrew Winslow, Tim Wylie
Abstract:
We analyze the complexity of building linear assemblies, sets of linear assemblies, and $\mathcal{O}(1)$-scale general shapes in the staged tile assembly model. For systems with at most $b$ bins and $t$ tile types, we prove that the minimum number of stages to uniquely assemble a $1 \times n$ \emph{line} is $\Theta(\log_t{n} + \log_b{\frac{n}{t}} + 1)$. Generalizing to $\BO{1} \times n$ lines, we prove the minimum number of stages is $\BO{\frac{\log{n} – tb – t\log t}{b^2} + \frac{\log \log b}{\log t}}$ and $\Omega(\frac{\log{n} – tb – t\log t}{b^2})$. We also obtain similar upper and lower bounds in a model permitting \emph{flexible glues} using non-diagonal glue functions.

Next, we consider assembling sets of lines and general shapes using $t = \BO{1}$ tile types. We prove that the minimum number of stages needed to assemble a set of $k$ lines of size at most $\BO{1} \times n$ is $\BO{\frac{k\log n}{b^2}+\frac{k\sqrt{\log n}}{b}+\log\log n}$ and $\Omega(\frac{k\log n}{b^2})$. In the case that $b = \BO{\sqrt{k}}$, the minimum number of stages is $\Theta(\log{n})$. The upper bound in this special case is then used to assemble “hefty” shapes of at least logarithmic edge-length-to-edge-count ratio at $\BO{1}$-scale using $\BO{\sqrt{k}}$ bins and optimal $\BO{\log{n}}$ stages.

Citation: Proc. of 17th Inter. Conf. on Unconventional Computation and Natural Computation (UCNC’18)
Bibtex:

Journal version in Natural Computing

The journal version of “Verification in Staged Tile Self-Assembly” was accepted for publication in Natural Computing. The conference version was published in UCNC 2017 last year. The authors are Robert Schweller, Andrew Winslow, and Tim Wylie.

Self-Assembly of Shapes at Constant Scale using Repulsive Forces

Self-Assembly of Shapes at Constant Scale using Repulsive Forces.
Austin Luchsinger, Robert Schweller, and Tim Wylie. In Natural Computing. 2018.

Link: https://link.springer.com/article/10.1007/s11047-018-9707-9

Abstract:

Bibtex:

 

Conference Version:

Self-Assembly of Shapes at Constant Scale using Repulsive Forces.
Austin Luchsinger, Robert Schweller, and Tim Wylie.
In Proc. of the 16th Inter. Conf. on Unconventional Computation and Natural Computation (UCNC’17), 2017.

Abstract:

Bibtex: