Asynchronous Signal Passing for Tile Self-Assembly: Fuel Efficient Computation and Efficient Assembly of Shapes

Active self-assembly of algorithmic shapes and patterns in polylogarithmic time

“…All of these models could be classed as passive in the sense that after some structure is grown, via a crystal-like growth process, the structure does not change. Active tile assembly models include the activatable tile model where tiles pass signals to each other and can change their internal 'state' based on other tiles that join to the assembly [53,54,37]. This interesting generalization of the tile assembly model is essentially an asynchronous nondeterministic cellular automaton of a certain kind, and may indeed be implementable using DNA origami tiles with strand displacement signals [53,54].…”

“…Active tile assembly models include the activatable tile model where tiles pass signals to each other and can change their internal 'state' based on other tiles that join to the assembly [53,54,37]. This interesting generalization of the tile assembly model is essentially an asynchronous nondeterministic cellular automaton of a certain kind, and may indeed be implementable using DNA origami tiles with strand displacement signals [53,54]. There are also models of algorithmic self-assembly where after a structure grows, tiles can be removed, such as the kinetic tile-assembly model [77,78,17] (which implements the chemical kinetics of tile assembly) and the negative-strength glue model [25,59,56], or the RNAse enzyme model [1,57,21].…”

Fuel Efficient Computation in Passive Self-Assembly

“…Recent work has introduced space-efficient, fuel-guzzling universal computation with the addition of negative glue interactions and the use of a powerful non-diagonal class of glue interactions [19]. Other recent work has shown how to achieve fuel efficient computation [27] within active tile self-assembly. In this paper we utilize negative interactions in the tile self-assembly model to achieve the first computationally universal passive tile self-assembly system that is both space and fuel-efficient.…”

“…al. [27] considers an active tile self-assembly model motivated by a DNA strand replacement mechanism in which tiles can pass simple, fire-once signals from one tile edge to another. They show that this simple mechanism allows for the implementation of fuel-efficient universal computation, as well as additional efficiencies that are provably impossible within the passive TAM.…”