So when a consensus protocol is in this kind of state where the network can affect which of several values can be output, we'll say that the protocol is in a bivalent state. Or you would maybe think multivalent, but I'm using bivalent to be consistent with the literature here.
So now here's an intuition behind this FLP impossibility result. Let's imagine that you have a terminating execution of a bivalent system. You start bivalent . Then eventually everybody outputs some value. And let's let m be the last message that was received by any node in a bivalent state.
And so if you cover yourself in carbohydrates, you're shielding yourself from antibodies. And that permits what we call bivalent binding between spike cross-linking.
So here's the overview of the FLP proof. You can show that there are bivalent starting configurations. And then if your system is fault tolerance, it turns out that the network can neutralize any deciding message.
And let's let m be the last message that was received by any node in a bivalent state. So receiving m is what flipped the system from a bivalent to a univalent state. So in that case, we'll call m the deciding message because somehow delivering m is what decided the fate of the system.
is in a bivalent state. Or you would maybe think multivalent, but I'm using bivalent to be consistent with the literature here. So conversely, you could reach a point where there's only one output value possible.
And, of course, all the output values need to agree. And so what that means is that it's never possible to output a value if you're in a bivalent state because once a particular value has been output, well, then that should seal the state of the system.
Any other output values should be the same. So that means that if you have one of these systems and you have an execution that starts in a bivalent state and then it eventually terminates, then it must at some point have reached a univalent state.
You start bivalent . Then eventually everybody outputs some value. And let's let m be the last message that was received by any node in a bivalent state. So receiving m is what flipped the system from a bivalent to a univalent state.
and pick a value. And so taken together, what these two things mean is that the system can essentially remain bivalent in perpetuity if every time there's about to be a deciding message the network pathologically delays just that one message until it's been neutralized.
So here, let's say we have eight candidate values, a through h. And initially, all the ballots in the system are bivalent . And then let's say the system agrees that they've prepared 1, g.
And so if you cover yourself in carbohydrates, you're shielding yourself from antibodies. And in that case, you'd have intra-spike cross-linking, which would allow bivalent binding, despite the fact that there's hardly any spikes
it must at some point have reached a univalent state. So now here's an intuition behind this FLP impossibility result. Let's imagine that you have a terminating execution of a bivalent system. You start bivalent . Then eventually everybody outputs some value.
So this is what voting actually gives us. If we try to use voting as a consensus protocol, we'll find that we start in some bivalent state. And then if we get enough votes, we might end up in an a valent state for some value a that we're voting Or we could end up in some a bar valent