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How does a host determine that his "clock does not work anymore?
I believe you mean by the clock does not work anymore is that the difference between the host and others are more than the expected difference. The purpose of the relative time protocol is to keep this difference small. So, as long as, the host runs the relative time, then his clock works always. If he was not able to run the relative time protocol because of e.g. disconnection or some other problem, then he can assume that his clock does not work anymore. So the short answer is that a host determines that his clock does not work anymore if he was not able to run the relative time protocol as specified.
I think a host can determine that he did not run the relative time protocol correctly when he sees in the final chain some blocks that he has never stored the arrival time of this block.
The basic idea of the algorithm is described in the research writeup.
However, to actually provide implementers with enough information to implement the algorithm, we will have to discuss the following open questions:
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