An Algebraic-Topological Approach to Processing Cross-Blockchain Transactions
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The state-of-the-art techniques for processing cross-blockchain transactions take 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 parties involved in a single global transaction, the global transaction is split into multiple local two-party transactions, each of which follows the above central-exchange protocol. Unfortunately, the atomicity of the global transaction is violated with the central-exchange approach: those local two-party transactions, once committed, cannot be rolled back if the global transaction decides to abort. In a more general sense, the graph-based model of (two-party) transactions can hardly be extended to an arbitrary number of parties in a cross-blockchain transaction. introduce a higher-level abstraction of cross-blockchain transactions. We adopt the abstract simplicial complex, an extensively-studied mathematical object in algebraic topology, to represent an arbitrary number of parties involved in the blockchain transactions. Essentially, each party in the global transaction is modeled as a vertex and the global transaction among n+1 (n ∈ℤ, n > 0) parties compose a n-dimensional simplex. While this higher-level abstraction seems plausibly trivial, we will show how this simple extension leads to a new line of modeling methods and protocols for better processing cross-blockchain transactions.
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