Covert Computation in the Abstract Tile-Assembly Model

There have been many advances in molecular computation that offer benefits such as targeted drug delivery, nanoscale mapping, and improved classification of nanoscale organisms. This power led to recent work exploring privacy in the computation, specifically, covert computation in self-assembling circuits. Here, we prove several important results related to the concept of a hidden computation in the most well-known model of self-assembly, the Abstract Tile-Assembly Model (aTAM). We show that in 2D, surprisingly, the model is capable of covert computation, but only with an exponential-sized assembly. We also show that the model is capable of covert computation with polynomial-sized assemblies with only one step in the third dimension (just-barely 3D). Finally, we investigate types of functions that can be covertly computed as members of P/Poly

Distributed Computation and Reconfiguration in Actively Dynamic Networks

We study here systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration to carry out a given task. Also, the distributed task itself may now require a global reconfiguration from a given initial network Gs to a target network Gf from a desirable family of networks. To formally capture costs associated with creating and maintaining connections, we define three edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. We give (poly)log(n) time algorithms for the task of transforming any Gs into a Gf of diameter (poly)log(n), while minimizing the edge-complexity. Our main lower bound shows that Ω(n) total edge activations and Ω(n/logn) activations per round must be paid by any algorithm (even centralized) that achieves an optimum of Θ(logn) rounds. We give three distributed algorithms for our general task. The first runs in O(logn) time, with at most 2n active edges per round, a total of O(nlogn) edge activations, a maximum degree n−1, and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations. It gives a target network of diameter O(logn) and uses O(n) active edges per round. Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve o(log2n) running time

Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 18331)

This report documents the program and the outcomes of Dagstuhl Seminar 18331,"Algorithmic Foundations of Programmable Matter", a new and emerging field that combines theoretical work on algorithms with a wide spectrum of practical applications that reach all the way from small-scale embedded systems to cyber-physical structures at nano-scale. The aim of this seminar was to bring together researchers from computational geometry, distributed computing, DNA computing, and swarm robotics who have worked on programmable matter to inform one another about the newest developments in each area and to discuss future models, approaches, and directions for new research. Similar to the first Dagstuhl seminar on programmable matter (16271), we did focus on some basic problems, but also considered new problems that were now within reach to be studied. During this seminar, we were able to achieve a previously unmatched level of intensity of collaboration, in part due to using a new electronic and interactive web-based platform. This has also allowed for continued research among the attendees based on the work begun during the seminar