Self-assembling Trees

AbstractRCCS is a variant of Milner's CCS where processes are allowed a controlled form of backtracking. It turns out that the RCCS reinterpretation of a CCS process is equivalent, in the sense of weak bisimilarity, to its causal transition system in CCS. This can be used to develop an efficient method for designing distributed algorithms, which we illustrate here by deriving a distributed algorithm for assembling trees. Such a problem requires solving a highly distributed consensus, and a comparison with a traditional CCS-based solution shows that the code we obtain is shorter, easier to understand, and easier to prove correct by hand, or even to verify

Computing multi-scale organizations built through assembly

The ability to generate and control assembling structures built over many orders of magnitude is an unsolved challenge of engineering and science. Many of the presumed transformational benefits of nanotechnology and robotics are based directly on this capability. There are still significant theoretical difficulties associated with building such systems, though technology is rapidly ensuring that the tools needed are becoming available in chemical, electronic, and robotic domains. In this thesis a simulated, general-purpose computational prototype is developed which is capable of unlimited assembly and controlled by external input, as well as an additional prototype which, in structures, can emulate any other computing device. These devices are entirely finite-state and distributed in operation. Because of these properties and the unique ability to form unlimited size structures of unlimited computational power, the prototypes represent a novel and useful blueprint on which to base scalable assembly in other domains. A new assembling model of Computational Organization and Regulation over Assembly Levels (CORAL) is also introduced, providing the necessary framework for this investigation. The strict constraints of the CORAL model allow only an assembling unit of a single type, distributed control, and ensure that units cannot be reprogrammed - all reprogramming is done via assembly. Multiple units are instead structured into aggregate computational devices using a procedural or developmental approach. Well-defined comparison of computational power between levels of organization is ensured by the structure of the model. By eliminating ambiguity, the CORAL model provides a pragmatic answer to open questions regarding a framework for hierarchical organization. Finally, a comparison between the designed prototypes and units evolved using evolutionary algorithms is presented as a platform for further research into novel scalable assembly. Evolved units are capable of recursive pairing ability under the control of a signal, a primitive form of unlimited assembly, and do so via symmetry-breaking operations at each step. Heuristic evidence for a required minimal threshold of complexity is provided by the results, and challenges and limitations of the approach are identified for future evolutionary studies

Self-assembling graphs

Abstract. A self-assembly algorithm for synchronising agents and have them arrange according to a particular graph is given. This algorithm, expressed using an ad hoc rule-based process algebra, extends Klavins ’ original proposal [1], in that it relies only on point-to-point communication, and can deal with any assembly graph whereas Klavins ’ method dealt only with trees. 1

On Self-Assembling Graphs in vitro

In this paper we identify a new type of structures that can be assembled in vitro by self-regulating molecular processes. This type of structure, the so-called automatic graphs, is a class of highly symmetric graphs Cayley graphs that have the same local appearance from every node and yet admit a finite-state navigator set that can discriminate global properties of the graph. We show how the navigator can be implemented as a molecule that directs the self-assembly process to build such graphs as nanostructures in DNA molecules. Cayley graphs form a class of highly regular structures that can, in principle, be used as read-only memories to support universal computation, even of super Turing type