Distributed Agreement in Tile Self-Assembly

TL;DR

This paper formalizes the connection between tile self-assembly and distributed computing, demonstrating how tile systems can simulate consensus problems and exploring the implications for fault-tolerance in nanoscale assembly.

Contribution

It introduces a formal framework linking tile assembly to distributed consensus, including simulation results for 2D and 3D models with varying process counts.

Findings

2D tile assembly simulates consensus for two processes.

3D tile assembly can simulate consensus for any number of processes.

A strengthened consensus problem is defined to clarify implicit assumptions.

Abstract

Laboratory investigations have shown that a formal theory of fault-tolerance will be essential to harness nanoscale self-assembly as a medium of computation. Several researchers have voiced an intuition that self-assembly phenomena are related to the field of distributed computing. This paper formalizes some of that intuition. We construct tile assembly systems that are able to simulate the solution of the wait-free consensus problem in some distributed systems. (For potential future work, this may allow binding errors in tile assembly to be analyzed, and managed, with positive results in distributed computing, as a "blockage" in our tile assembly model is analogous to a crash failure in a distributed computing model.) We also define a strengthening of the "traditional" consensus problem, to make explicit an expectation about consensus algorithms that is often implicit in distributed computing literature. We show that solution of this strengthened consensus problem can be simulated by a two-dimensional tile assembly model only for two processes, whereas a three-dimensional tile assembly model can simulate its solution in a distributed system with any number of processes.