Abstract: Blockchain has experienced rapid development, giving rise to a variety of underlying platforms. However, whether applications are built on the same or different platforms, achieving seamless cross-platform interoperability and collaboration remains a significant challenge. Against this backdrop, cross-chain technology for building trusted inter-chain interaction channels has gradually become the focus of attention in the industry. Despite this growing interest, both academia and industry lack a unified and accurate definition of cross-chain transactions. Existing cross-chain technologies mainly focus on asset exchange and swap scenarios but suffer from insufficient universality, fragmented key technologies, and inconsistent implementation methods. Aiming at the above problems, this paper analyzes current mainstream cross-chain technologies, proposes a formal definition of general blockchain cross-chain transaction, and designs a cross-chain algorithm based on this definition taking asset exchange cross-chain mode as an example. Finally, the above algorithm is validated using existing classic cross-chain platforms such as BitXHub and Polkadot. Experimental results show that the formal definition and cross-chain algorithm proposed in this paper can not only provide guidance for improving existing platforms, but also offer effective references for future data-based cross-chain platforms that have not yet appeared or have not been applied in practice.

Key words: blockchain, cross-chain, asset exchange, data interoperability, business collaboration, formalization