Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks

TL;DR

This paper explores how simple chemical reaction networks can undergo dramatic phase transitions at certain population levels, complicating their verification, but demonstrates how formal theorem provers can effectively verify such systems.

Contribution

It introduces a method for verifying population-induced phase transitions in chemical reaction networks using formal theorem proving, overcoming limitations of traditional methods.

Findings

Chemical reaction networks can exhibit phase transitions at specific population thresholds.

Traditional simulation and model checking methods may fail to verify behaviors at realistic populations.

Formal theorem provers can successfully verify systems where other methods fail.

Abstract

We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts to use simulation, model checking, or approximation by differential equations to formally verify the behaviors of such systems at realistic populations. We show how formal theorem provers can successfully verify some such systems at populations where other verification methods fail.