Property-paths-to-other-voted-anchor
Property that if an anchor in a DAG has enough votes
then all the certificates in any other DAG
that are at leaast two rounds after the anchor
have some path to the anchor, which is also in the other DAG.
This is similar to property-paths-to-voted-anchor,
but concerns two DAGs of different validators.
The same intersection argument applies across validators:
given a certificate (anchor) A in DAG 1 at round r,
with at least F+1 voters for A in DAG 1 at round r+1,
and N-F certificates in DAG 2 at round r+1,
every certificate C in DAG 2 at round r+2 or later
has a path to A, which must be also in DAG 2.
The reason is that there must be a certificate B
that is both in the F+1 or more voters in DAG 1
and in the N-F certificates in DAG 2.
In DAG 1, it has an edge to A.
Because of the backward closure of DAG 2,
A must be in DAG 2 too, with an edge to it from B.
Since B is a predecessor of C,
there is a path from C to A.
This holds for every C in DAG 2 in round r+2,
so every D in DAG 2 at round r+3
has a predecessor C with a path to A
and so D has a path to A too.
And so on for the rest of the rounds of DAG2.
Subtopics
- Dag-all-path-to-p-other-holds
- This is the property
described in property-paths-to-voted-anchor.