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This paper rigorously proves that Bitcoin can achieve consensus under the assumption of bounded message delivery time:

Messages in a mailbox may be delivered in any order, and at any time, except there is a maximum delay of ∆

If I understand it correctly, this only proves it works in synchronous network. If so, this assumption seems relaxed to me.

Tendermint paper claims it can work under the partial synchronous assumption (from DLS paper):

There is assumed to be some unknown upper bound ∆ on the time of messages to be delivered.

The setup is more general in that the upper bound ∆ here is unknown.

Can Bitcoin protocol achieve consensus in partial synchronous network as well? Is there any theory work dedicated to proving that?

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If I understand it correctly, this only proves it works in synchronous network. If so, this assumption seems relaxed to me.

The Bitcoin network is not synchronous, it is asynchronous and maintains consensus.

Can Bitcoin protocol achieve consensus in partial synchronous network as well?

Since Bitcoin is an asynchronous network and achieves consensus, it stands to reason that Bitcoin would be able to achieve consensus in a synchronous or partially synchronous network as well.

  • I guess with plain English is not precise enough for discussion. There's so much subtle differences between different types of synchrony. Like the max message deliver delay assumption. The fact that it "works" most of the time in real life doesn't prove it will always work. Only rigorous proof can convince me. – user10375 Jan 15 '18 at 3:02
  • There is no proof that Bitcoin achieves consensus in an asynchronous network (yet), so we don't know whether it does, or what additional assumptions are needed. – Pieter Wuille Sep 3 '18 at 1:15
  • A proof for consensus under synchronous assumptions is mostly vacuous: More or less equivalent to showing a digital signature scheme is secure against forgery in a universe where the only way to generate a signature is to follow the protocol. Formalization that show Bitcoin secure under contrived models might be useful progress, but aren't actually evidence of security in a useful sense. I am very concerned about the ethics of some parties that show Bitcoin secure in a toy formalization then argue an alternative is equally secure because it is also secure in the same toy formalization. – G. Maxwell Oct 16 '18 at 1:05
  • @G.Maxwell, does bitcoin not assume that all peer clocks are synchronized within 2 hours? That is my node will reject blocks 2 hours into future, so there is some synchronization assumption, right? – sanket1729 Oct 17 '18 at 0:42

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