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Note a more efficient computation of the auth difference.

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David Robertson 2022-06-13 15:59:34 +01:00
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content/rooms/fragments/v2-state-res.md
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@ -45,15 +45,19 @@ whereas the conflicted state set may associate multiple events to the same key.
The *auth chain* of an event *E* is the set containing all of *E*'s auth events, The *auth chain* of an event *E* is the set containing all of *E*'s auth events,
all of *their* auth events, and so on recursively, stretching back to the all of *their* auth events, and so on recursively, stretching back to the
start of the room. Put differently, these are the events reachable by walking start of the room. Put differently, these are the events reachable by walking
the graph induced by an event's `auth_events` links. the graph induced by an event's `auth_events` links. If *S* is a collection of
events, the *full auth chain of S* is the union of the auth chains of every
event *E* in *S*.
**Auth difference.** **Auth difference.**
The *auth difference* is calculated by first calculating the full auth The *auth difference* is calculated by first calculating the full auth
chain for each state *S*<sub>*i*</sub>, that is the union of the auth chain for each state *S*<sub>*i*</sub>, and then discarding the events
chains for each event in *S*<sub>*i*</sub>, and then taking every event belonging to each full auth chain. In symbols: if *C*(*S*) is the full auth
that doesn't appear in every auth chain. If *C*<sub>*i*</sub> is the chain of a collection of events *S*, the auth difference is
full auth chain of *S*<sub>*i*</sub>, then the auth difference is ∪<sub>*i*</sub> *C*(*S<sub>i*</sub>) - ∩<sub>*i*</sub> *C*(*S<sub>i</sub>*).
 ∪ *C*<sub>*i*</sub> −  ∩ *C*<sub>*i*</sub>. This can be [computed more efficiently](https://github.com/matrix-org/matrix-spec/issues/1118) as
*C*(*F*) - ∩<sub>*i*</sub> *C*(*S<sub>i* - *F*) ,
where *F* is the full conflicted set.
**Full conflicted set.** **Full conflicted set.**
The *full conflicted set* is the union of the conflicted state set and The *full conflicted set* is the union of the conflicted state set and