What is their argument that PoW doesn’t work under asynchronous setting? This paper already proved that it does work: https://eprint.iacr.org/2016/454.pdf
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Check section 8. What that paper means by working under async setting is not really fully async, but async *with an upper bound on network delays* - which is really semi-sync.
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I wouldn't say it is synchronous nor even semi-sync. I would say it is asynchronous to a certain extent. It is still asynchronous simply because there's no global clock.
End of conversation
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