On the Simulation Power of Surface Chemical Reaction Networks

TL;DR

The paper establishes a rigorous bridge between surface chemical reaction networks (sCRNs) and several well-studied distributed computation models by proving mutual simulations under carefully defined representations. It introduces an orientation-coloring technique that resolves the intrinsic lack of global direction in sCRNs and demonstrates that unit-seeded sCRNs can simulate directed sCRNs, aTAM, tile automata with affinity-strengthening, asynchronous CA, and Amoebot, and vice versa. The key contributions include a suite of structured simulation protocols, proof sketches of inter-model simulations, and a coherent framework for comparing heterogeneous computational paradigms through formal reductions. This cross-model universality highlights the robustness of local interaction rules in achieving global computational power and pattern formation across diverse physical substrates. The results have implications for understanding programmable matter and molecular computing, showing that spatially constrained reaction networks can emulate classic computational models and vice versa, enabling transfers of techniques and complexity results across domains.

Abstract

The Chemical Reaction Network (CRN) is a well-studied model that describes the interaction of molecules in well-mixed solutions. In 2014, Qian and Winfree [22] proposed the abstract surface chemical reaction network model (sCRN), which takes the advantage of spatial separation by placing molecules on a structured surface, limiting the interaction between molecules. In this model, molecules can only react with their immediate neighbors. Many follow up works study the computational and pattern-construction power of sCRNs. In this work, our goal is to describe the power of sCRN by relating the model to other well-studied models in distributed computation. In this work, our main result is to show that, given the same initial configuration, sCRN, affinity strengthening tile automata, cellular automata, and amoebot can all simulate each other (up to unavoidable rotation and reflection of the pattern). One of our techniques is a coloring on-the-fly, which allows all molecules in sCRN to have a global orientation.

Figures (8)

• Figure 1: Coloring the block of the seed by
• Figure 2: An example of the simulation of a growing reaction.
• Figure 3: Tile species and observing species.
• Figure 4: A simple example of simulating attachment.
• Figure 5: Simulation of acync-CA on sCRN.

Theorems & Definitions (22)

• definition thmcounterdefinition
• definition thmcounterdefinition
• definition thmcounterdefinition
• definition thmcounterdefinition
• theorem thmcountertheorem
• lemma thmcounterlemma
• proof
• lemma thmcounterlemma
• lemma thmcounterlemma
• proof