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Jeff Burdges
2018-11-08 23:26:51 +01:00
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pdf/grandpa.tex
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@@ -122,7 +122,7 @@ Casper...
There are two main differences between Casper FFG and GRANDPA. One is that in GRANDPA, different voters can cast votes simultaneously for blocks at different heights. There are two main differences between Casper FFG and GRANDPA. One is that in GRANDPA, different voters can cast votes simultaneously for blocks at different heights.
The other main difference is how the finality gadget affects the fork-choice rule of the underlying block production mechanism. In GRANDPA, by default we will assume that this is only affected by having to include any finalised blocks. The other main difference is how the finality gadget affects the fork-choice rule of the underlying block production mechanism. In GRANDPA, by default we will assume that this is only affected by having to include any finalised blocks.
\cite{CasperFFG} does not specify a fork-choice rule, but it requires that we build on justified blocks for liveness. Later specifications of Casper use the GHOST rule on votes for fork-choice. Casper FFG \cite{CasperFFG} does not specify a fork-choice rule, but it requires that we build on justified blocks for liveness. Later specifications of Casper use the GHOST rule on votes for fork-choice.
Only depending on finalised blocks gives a clearer separation between the block production mechanism and finality gadget. It may therefore be easier to adapt to other types of protocol that achieve eventual consensus—and there have been many diverse protocols that do this developed in the last few years. It also makes it far easier to prove liveness properties. If the finality gadget has not finalised anything and so does not interfere, then the underlying mechanism should reach eventual consensus, which should be enough for the finality gadget to finalise whatever we have consensus on. Only depending on finalised blocks gives a clearer separation between the block production mechanism and finality gadget. It may therefore be easier to adapt to other types of protocol that achieve eventual consensus—and there have been many diverse protocols that do this developed in the last few years. It also makes it far easier to prove liveness properties. If the finality gadget has not finalised anything and so does not interfere, then the underlying mechanism should reach eventual consensus, which should be enough for the finality gadget to finalise whatever we have consensus on.
@@ -175,10 +175,9 @@ Note that we can easily update $g(S)$ to $g(S \cup \{v\})$, by checking if any c
3 tells us that even if validators see different subsets of the votes cast in a given voting round, this rule may give them different blocks but all such blocks are in the same chain under this assumption. 3 tells us that even if validators see different subsets of the votes cast in a given voting round, this rule may give them different blocks but all such blocks are in the same chain under this assumption.
We say that it is possible for a set $S$ to have a supermajority for $B$ if $2f+1$ validators either vote for a block $\not \geq B$ or equivocate in $S$. Note that if $S$ is tolerant, it is possible for $S$ to have a supermajority for $B$ if and only if there is a tolerant $T \supseteq S$ that has a supermajority for $B$. We say that it is {\em possible} for a set $S$ to have a supermajority for $B$ if $2f+1$ validators either vote for a block $\not \geq B$ or equivocate in $S$. Note that if $S$ is tolerant, it is possible for $S$ to have a supermajority for $B$ if and only if there is a tolerant $T \supseteq S$ that has a supermajority for $B$.
We say that it is {\em impossible} for any child of $B$ to have a supermajority in $S$ if $S$ has votes from at least $2f+1$ validators and it is impossible for $S$ to have a supermajority for each child of $B$ appearing on the chain of any vote in $S$. Again, provided $S$ is tolerant, this holds if and only if for any possible child of $B$, there is no tolerant $T \subseteq S$ that has a supermajority for that child.
We say that it is impossible for any child of $B$ to have a supermajority in $S$ if $S$ has votes from at least $2f+1$ validators and it is impossible for $S$ to have a supermajority for each child of $B$ appearing on the chain of any vote in $S$. Again, provided $S$ is tolerant, this holds if and only if for any possible child of $B$, there is no tolerant $T \subseteq S$ that has a supermajority for that child.
Note that it is possible for an intolerant $S$ to both have a supermajority for $S$ and for it to be impossible to have such a supermajority under these definitions, as we regard such sets as impossible anyway. Note that it is possible for an intolerant $S$ to both have a supermajority for $S$ and for it to be impossible to have such a supermajority under these definitions, as we regard such sets as impossible anyway.