Abstract
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.
This research was supported in part by National Science Foundation Grant CCF-1817602.
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Notes
- 1.
Typical TA models are defined with a temperature parameter \(\tau \) however, with consideration of solely 1D, eliminating the possibility of cooperative binding, we assume \(\tau = 1\).
- 2.
Each bin may be seen as an instance of the 2-Handed Assembly Model.
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Cirlos, S.C., Gomez, T., Grizzell, E., Rodriguez, A., Schweller, R., Wylie, T. (2023). Simulation of Multiple Stages in Single Bin Active Tile Self-assembly. In: Genova, D., Kari, J. (eds) Unconventional Computation and Natural Computation. UCNC 2023. Lecture Notes in Computer Science, vol 14003. Springer, Cham. https://doi.org/10.1007/978-3-031-34034-5_11
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