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

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.