Intrinsic Universality in Seeded Active Tile Self-Assembly

TL;DR

This paper demonstrates that seeded Tile Automata can serve as a universal model for self-assembly, capable of simulating any other TA system's output, dynamics, and internal states in a non-committal, non-deterministic manner.

Contribution

It introduces a single universal Tile Automata system with approximately 4600 states that can simulate any other TA system's behavior, including assembly output, dynamics, and internal states, in a non-committal way.

Findings

Universal TA system can simulate any TA system.

The system preserves non-deterministic dynamics.

Transferable to pairwise Cellular Automata.

Abstract

The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system G, (b) the dynamics involved in building G's assemblies, and (c) G's internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile's potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection. The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in G, transferring the information to simulate G to each new tile. Supertiles may also asynchronously transition states according to the rules of G. This result directly transfers to a restricted version of asynchronous Cellular Automata: pairwise Cellular Automata.