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Regarding the fact that in Proof-of-Stake, a stakeholder will be elected randomly as the next author of the next block in each epoch (or each round or slot), logically, in each round (or slot) there is only a single author of block, and so a single proposed block. With these conditions, and whether this new block will be validate or not by the rest of the network, is there still the possibility of occurring a fork in each round? (As in each round a single author is selected.)

IMPORTANT : In this question, I mean "slot" by saying "round" and "epoch".

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Proof-of-Stake: How to prevent someone from being always selected as an author of block?

How to select the next author of block in Proof-of-Stake?

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Yes, forks are possible in Proof of Stake.

Here is an example. Assume Alice (A) is the proposer for slot 1 and Bob (B) for slot 2. The genesis (G) block is slot 0.

Alice creates the block at slot 1. This chain is G->A.

Bob never saw Alice's block so he creates the block at slot 2. This chain is G->empty->B.

There's now 2 forks. Charlie, the proposer in slot 3, can choose between either fork. (There is also a chance that Charlie could choose neither fork, and a third fork could be G->empty->empty->C.)

See What's the difference between a Slot and a Block?

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    But I meant in each slot. In the question, I wrote: in each round that I meant slot. So, Can we say that in each slot, there is no fork? Thanks – Questioner Sep 18 '20 at 10:42
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    Alice could propose more than one block in slot 1. But she will likely get slashed, which would lead to her getting ejected and banned from being a validator. A technical paper you may be interested in about the topic: arxiv.org/abs/2003.03052 – eth♦ Sep 21 '20 at 10:23
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    @Questioner No, since there's a fork in slot 1 in this example -- does it contain block A or is it empty? Unless the plan is to wait forever for a block, there can always be disagreement over whether a block was placed in that slot or whether the timeout expired. That is a fork as someone who thinks a block was placed in that slot might rely on a transaction in that block being accepted. – David Schwartz Feb 23 at 18:03

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