Towards Universal Atomic Composability: A Formal Model for Multi-Rollup Environments on Ethereum

This paper introduces a formal framework for analyzing atomic composability in multi-rollup environments on Ethereum. As the blockchain ecosystem evolves towards a multi-rollup future, ensuring atomic execution of cross-rollup transactions becomes increasingly critical. We present a mathematical model that formally defines atomic composability in this context and establish necessary conditions for achieving it across different rollup systems.

Our work makes several key contributions:

• A formal definition of universal atomic composability for multi-rollup environments
• A mathematical framework for analyzing cross-rollup transaction properties
• Proof of necessary and sufficient conditions for atomic execution
• Analysis of existing cross-rollup protocols against our formal model

The findings have important implications for the design of cross-rollup bridges and protocols, suggesting new approaches for achieving robust composability in the growing rollup ecosystem.