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I am learning the fundamental of Proof of Stake (PoS), i came accross a question which i could not find answer to. Assume we have three validators (aka miners in PoW), V1, V2 and V3. Each of the validators controls 1/3 of the total stake? If PoS is designed to have a block generated each 5 seconds. at time=5 V1 was assigned to generate a block B1 and send it to other verifiers. Due to propagation delay, V2 was assigned to generated B2 at time =10, but at that time he has not received B1 yet .

In PoW, V2 will generate another version of B1 "a competitive block", so this refers to a fork, and at the end either V1 or V2 will win the block.

My question, does this will be the case for PoS? if not, how it works then?

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yes that's the case for PoS it will fork into 2 branch and the job of PoS is to choose which chain to follow. The way to do it is different for every protocol like in casper ffg:

FOLLOW THE CHAIN CONTAINING THE JUSTIFIED CHECKPOINT OF THE GREATEST HEIGHT

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