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The state-of-the-art techniques for processing cross-blockchain transactionstake a simple centralized approach: when the assets on blockchain $X$, say$X$-coins, are exchanged with the assets on blockchain $Y$---the $Y$-coins,those $X$-coins need to be exchanged to a "middle" medium (such as Bitcoin)that is then exchanged to $Y$-coins. If there are more than two partiesinvolved in a single global transaction, the global transaction is split intomultiple local two-party transactions, each of which follows the abovecentral-exchange protocol. Unfortunately, the atomicity of the globaltransaction is violated with the central-exchange approach: those localtwo-party transactions, once committed, cannot be rolled back if the globaltransaction decides to abort. In a more general sense, the graph-based model of(two-party) transactions can hardly be extended to an arbitrary number ofparties in a cross-blockchain transaction. %from why to how In this paper, weintroduce a higher-level abstraction of cross-blockchain transactions. We adoptthe \textit{abstract simplicial complex}, an extensively-studied mathematicalobject in algebraic topology, to represent an arbitrary number of partiesinvolved in the blockchain transactions. Essentially, each party in the globaltransaction is modeled as a vertex and the global transaction among $n+1$ ($n\in \mathbb{Z}$, $n > 0$) parties compose a $n$-dimensional simplex. While thishigher-level abstraction seems plausibly trivial, we will show how this simpleextension leads to a new line of modeling methods and protocols for betterprocessing cross-blockchain transactions.

An Algebraic-Topological Approach to Processing Cross-Blockchain Transactions