Doubles and Negatives are Positive (in Self-Assembly)

In the abstract Tile Assembly Model (aTAM), the phenomenon of cooperation occurs when the attachment of a new tile to a growing assembly requires it to bind to more than one tile already in the assembly. Often referred to as ``temperature-2'' systems, those which employ cooperation are known to be quite powerful (i.e. they are computationally universal and can build an enormous variety of shapes and structures). Conversely, aTAM systems which do not enforce cooperative behavior, a.k.a. ``temperature-1'' systems, are conjectured to be relatively very weak, likely to be unable to perform complex computations or algorithmically direct the process of self-assembly. Nonetheless, a variety of models based on slight modifications to the aTAM have been developed in which temperature-1 systems are in fact capable of Turing universal computation through a restricted notion of cooperation. Despite that power, though, several of those models have previously been proven to be unable to perform or simulate the stronger form of cooperation exhibited by temperature-2 aTAM systems. In this paper, we first prove that another model in which temperature-1 systems are computationally universal, namely the restricted glue TAM (rgTAM) in which tiles are allowed to have edges which exhibit repulsive forces, is also unable to simulate the strongly cooperative behavior of the temperature-2 aTAM. We then show that by combining the properties of two such models, the Dupled Tile Assembly Model (DTAM) and the rgTAM into the DrgTAM, we derive a model which is actually more powerful at temperature-1 than the aTAM at temperature-2. Specifically, the DrgTAM, at temperature-1, can simulate any aTAM system of any temperature, and it also contains systems which cannot be simulated by any system in the aTAM

Spartan Daily, March 23, 1984

Volume 82, Issue 38https://scholarworks.sjsu.edu/spartandaily/7156/thumbnail.jp

Spartan Daily, February 23, 1981

Volume 76, Issue 19https://scholarworks.sjsu.edu/spartandaily/6723/thumbnail.jp

Spartan Daily, March 20, 1974

Volume 62, Issue 22https://scholarworks.sjsu.edu/spartandaily/5845/thumbnail.jp

Spartan Daily, May 1, 1981

Volume 76, Issue 62https://scholarworks.sjsu.edu/spartandaily/6766/thumbnail.jp

Powers and Behaviors of Directed Self-assembly

In nature there are a variety of self-assembling systems occurring at varying scales which give rise to incredibly complex behaviors. Theoretical models of self-assembly allow us to gain insight into the fundamental nature of self-assembly independent of the specific physical implementation. In Winfree\u27s abstract tile assembly model (aTAM), the atomic components are unit square tiles which have glues on their four sides. Beginning from a seed assembly, these tiles attach one at a time during the assembly process in an asynchronous and nondeterministic manner. We can gain valuable insights into the nature of self-assembly by comparing different models of self-assembly which use fundamentally different mechanisms for local interactions. A powerful notion which allows us to compare models of self-assembly is simulation. The first result of this thesis examines the role of non-determinism in simulation. It shows that the universal simulation of directed aTAM systems requires undirectedness. A tile assembly model is said to be directed if it always assembles the same final assembly. We distinguish between two types of aTAM systems: cooperative systems and non-cooperative systems. In cooperative aTAM systems, we are able to enforce that in order for a tile to attach to an assembly, the glues of a tile must match two or more glues of neighboring tiles. On the other hand, in non-cooperative aTAM systems, tiles are able to attach to an assembly provided that one of the tile\u27s glues match an exposed glue on the assembly. It is well known that the cooperative aTAM is computationally universal, and it is conjectured that the non-cooperative aTAM is not computationally universal. For our second result, we show that if we allow tiles to be polygons with six or more sides, then the class of non-cooperative systems is capable of universal computation. On the other hand, we show that the class of systems consisting of polygons with six or less sides is not capable of computing using any of the currently known methods

Universal Computation with Arbitrary Polyomino Tiles in Non-Cooperative Self-Assembly

In this paper we explore the power of geometry to overcome the limitations of non-cooperative self-assembly. We define a generalization of the abstract Tile Assembly Model (aTAM), such that a tile system consists of a collection of polyomino tiles, the Polyomino Tile Assembly Model (polyTAM), and investigate the computational powers of polyTAM systems at temperature 1, where attachment among tiles occurs without glue cooperation (i.e., without the enforcement that more than one tile already existing in an assembly must contribute to the binding of a new tile). Systems composed of the unit-square tiles of the aTAM at temperature 1 are believed to be incapable of Turing universal computation (while cooperative systems, with temperature \u3e 1, are able). As our main result, we prove that for any polyomino P of size 3 or greater, there exists a temperature-1 polyTAM system containing only shape-P tiles that is computationally universal. Our proof leverages the geometric properties of these larger (relative to the aTAM) tiles and their abilities to effectively utilize geometric blocking of particular growth paths of assemblies, while allowing others to complete. In order to prove the computational powers of polyTAM systems, we also prove a number of geometric properties held by all polyominoes of size ≥ 3. To round out our main result, we provide strong evidence that size-1 (i.e. aTAM tiles) and size-2 polyomino systems are unlikely to be computationally universal by showing that such systems are incapable of geometric bitreading, which is a technique common to all currently known temperature-1 computationally universal systems. We further show that larger polyominoes with a limited number of binding positions are unlikely to be computationally universal, as they are only as powerful as temperature-1 aTAM systems. Finally, we connect our work with other work on domino self-assembly to show that temperature-1 assembly with at least 2 distinct shapes, regardless of the shapes or their sizes, allows for universal computation

An investigation of the needs and the design of an orbiting space station with growth capabilities

An architectural approach to the evolutionary growth of an orbiting space station from a small manned satellite to a fully independent, self-sustainable space colony facility is presented. Social and environmental factors, ease of transportation via the space shuttle, and structural design are considered