Topological Properties of Multi-Party Blockchain Transactions

TL;DR

This paper introduces a topological framework to analyze and reason about the complex behavior of multi-party cross-blockchain transactions, addressing the challenges posed by blockchain forks and nondeterminism.

Contribution

It develops a systematic topological approach to model and analyze cross-blockchain transactions and forks, providing new insights into transaction outcomes.

Findings

Topological spaces for transactions and forks are constructed.

These spaces are related through homeomorphisms or continuous functions.

The growing-fork topology offers an intuitive representation of blockchain behavior.

Abstract

The cross-blockchain transaction remains one of the most challenging problems in blockchains. The root cause of the challenge lies in the nondeterministic nature of blockchains: A $n$-party transaction across multiple blockchains might be partially rolled back due to the potential forks in any of the participating blockchains---eventually, only one fork will survive in the competition among miners. While some effort has recently been made to developing hierarchically distributed commit protocols to make multi-party transactions progress, there is no systematic method to reason about the transaction outcome. This paper tackles this problem from a perspective of point-set topology. We construct multiple topological spaces for the transactions and blockchain forks, and show that these spaces are internally related through either homeomorphism or continuous functions. Combined together, these tools allow us to reason about the cross-blockchain transactions through the growing-fork topology, an intuitive representation of blockchains.