In this paper, we consider the problem of cross-chain payment whereby customers of different escrows—implemented by a bank or a blockchain smart contract—successfully transfer digital assets without trusting each other. Prior to this work, cross-chain payment problems did not require this success, or any form of progress. We introduce a new specification formalism called Asynchronous Networks of Timed Automata to formalise such protocols. We present the first cross-chain payment protocol that ensures termination in a bounded amount of time and works correctly in the presence of clock drift. We then demonstrate that it is impossible to solve this problem without assuming synchrony, in the sense that each message is guaranteed to arrive within a known amount of time. Yet, we solve an eventually terminating weaker variant of this problem, where success is conditional on the patience of the participants, without assuming synchrony, and in the presence of Byzantine failures. We also discuss the relation with the recently defined cross-chain deals.

在本文中，我们考虑了跨链支付问题，即不同托管机构的客户（由银行或区块链智能合约实施）在彼此不信任的情况下成功转移数字资产。在这项工作之前，跨链支付问题并不需要这种成功，或任何形式的进步。我们引入了一种新的规范形式主义，称为定时自动机的异步网络使此类协议正式化。我们提出了第一个跨链支付协议，该协议可确保在有限的时间内终止并在存在时钟漂移的情况下正常工作。然后我们证明如果不假设同步就不可能解决这个问题，因为每条消息都保证在已知的时间内到达。然而，我们解决了这个问题的一个最终终止的较弱变体，其中成功取决于参与者的耐心，没有假设同步，并且存在拜占庭失败。我们还讨论了与最近定义的跨链交易的关系。