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The cross-blockchain transaction remains one of the most challenging problemsin blockchains. The root cause of the challenge lies in the nondeterministicnature of blockchains: A $n$-party transaction across multiple blockchainsmight be partially rolled back due to the potential forks in any of theparticipating blockchains---eventually, only one fork will survive in thecompetition among miners. While some effort has recently been made todeveloping hierarchically distributed commit protocols to make multi-partytransactions progress, there is no systematic method to reason about thetransaction outcome. This paper tackles this problem from a perspective ofpoint-set topology. We construct multiple topological spaces for thetransactions and blockchain forks, and show that these spaces are internallyrelated through either homeomorphism or continuous functions. Combinedtogether, these tools allow us to reason about the cross-blockchaintransactions through the growing-fork topology, an intuitive representation ofblockchains.

Topological Properties of Multi-Party Blockchain Transactions