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# Room Version 2

This room version builds off of version 1 with an improved state resolution algorithm.

## Server implementation components

Room version 2 uses the base components of room version 1, changing only the state resolution algorithm.

### State resolution

The room state *S*′(*E*) after an event *E* is defined in terms of the
room state *S*(*E*) before *E*, and depends on whether *E* is a state
event or a message event:

- If
*E*is a message event, then*S*′(*E*) =*S*(*E*). - If
*E*is a state event, then*S*′(*E*) is*S*(*E*), except that its entry corresponding to*E*’s`event_type`

and`state_key`

is replaced by*E*’s`event_id`

.

The room state *S*(*E*) before *E* is the *resolution* of the set of
states {*S*′(*E*_{1}), *S*′(*E*_{2}), …} consisting of
the states after each of *E*’s `prev_event`

s
{*E*_{1}, *E*_{2}, …}, where the resolution of a set of
states is given in the algorithm below.

#### Definitions

The state resolution algorithm for version 2 rooms uses the following
definitions, given the set of room states
{*S*_{1}, *S*_{2}, …}:

Power events

A *power event* is a state event with type `m.room.power_levels`

or
`m.room.join_rules`

, or a state event with type `m.room.member`

where
the `membership`

is `leave`

or `ban`

and the `sender`

does not match the
`state_key`

. The idea behind this is that power events are events that
might remove someone’s ability to do something in the room.

Unconflicted state map and conflicted state set

The *unconflicted state map* is the state where the value of each key
exists and is the same in each state *S*_{i}. The *conflicted
state set* is the set of all other state events. Note that the
unconflicted state map only has one event per `(event_type, state_key)`

,
whereas the conflicted state set may have multiple events.

Auth difference

The *auth difference* is calculated by first calculating the full auth
chain for each state *S*_{i}, that is the union of the auth
chains for each event in *S*_{i}, and then taking every event
that doesn’t appear in every auth chain. If *C*_{i} is the
full auth chain of *S*_{i}, then the auth difference is
∪ *C*_{i} − ∩ *C*_{i}.

Full conflicted set

The *full conflicted set* is the union of the conflicted state set and
the auth difference.

Reverse topological power ordering

The *reverse topological power ordering* of a set of events is the
lexicographically smallest topological ordering based on the DAG formed
by auth events. The reverse topological power ordering is ordered from
earliest event to latest. For comparing two topological orderings to
determine which is the lexicographically smallest, the following
comparison relation on events is used: for events *x* and *y*,
*x* < *y* if

*x*’s sender has*greater*power level than*y*’s sender, when looking at their respective`auth_event`

s; or- the senders have the same power level, but
*x*’s`origin_server_ts`

is*less*than*y*’s`origin_server_ts`

; or - the senders have the same power level and the events have the same
`origin_server_ts`

, but*x*’s`event_id`

is*less*than*y*’s`event_id`

.

The reverse topological power ordering can be found by sorting the events using Kahn’s algorithm for topological sorting, and at each step selecting, among all the candidate vertices, the smallest vertex using the above comparison relation.

Mainline ordering

Given an `m.room.power_levels`

event *P*, the *mainline of* *P* is the
list of events generated by starting with *P* and recursively taking the
`m.room.power_levels`

events from the `auth_events`

, ordered such that
*P* is last. Given another event *e*, the *closest mainline event to*
*e* is the first event encountered in the mainline when iteratively
descending through the `m.room.power_levels`

events in the `auth_events`

starting at *e*. If no mainline event is encountered when iteratively
descending through the `m.room.power_levels`

events, then the closest
mainline event to *e* can be considered to be a dummy event that is
before any other event in the mainline of *P* for the purposes of
condition 1 below.

The *mainline ordering based on* *P* of a set of events is the ordering,
from smallest to largest, using the following comparison relation on
events: for events *x* and *y*, *x* < *y* if

- the closest mainline event to
*x*appears*before*the closest mainline event to*y*; or - the closest mainline events are the same, but
*x*’s`origin_server_ts`

is*less*than*y*’s`origin_server_ts`

; or - the closest mainline events are the same and the events have the
same
`origin_server_ts`

, but*x*’s`event_id`

is*less*than*y*’s`event_id`

.

Iterative auth checks

The *iterative auth checks algorithm* takes as input an initial room
state and a sorted list of state events, and constructs a new room state
by iterating through the event list and applying the state event to the
room state if the state event is allowed by the authorization
rules.
If the state event is not allowed by the authorization rules, then the
event is ignored. If a `(event_type, state_key)`

key that is required
for checking the authorization rules is not present in the state, then
the appropriate state event from the event’s `auth_events`

is used if
the auth event is not rejected.

#### Algorithm

The *resolution* of a set of states is obtained as follows:

- Take all
*power events*and any events in their auth chains, recursively, that appear in the*full conflicted set*and order them by the*reverse topological power ordering*. - Apply the
*iterative auth checks algorithm*, starting from the*unconflicted state map*, to the list of events from the previous step to get a partially resolved state. - Take all remaining events that weren’t picked in step 1 and order them by the mainline ordering based on the power level in the partially resolved state obtained in step 2.
- Apply the
*iterative auth checks algorithm*on the partial resolved state and the list of events from the previous step. - Update the result by replacing any event with the event with the
same key from the
*unconflicted state map*, if such an event exists, to get the final resolved state.

#### Rejected events

Events that have been rejected due to failing auth based on the state at the event (rather than based on their auth chain) are handled as usual by the algorithm, unless otherwise specified.

Note that no events rejected due to failure to auth against their auth chain should appear in the process, as they should not appear in state (the algorithm only uses events that appear in either the state sets or in the auth chain of the events in the state sets).

This helps ensure that different servers' view of state is more likely to converge, since rejection state of an event may be different. This can happen if a third server gives an incorrect version of the state when a server joins a room via it (either due to being faulty or malicious). Convergence of state is a desirable property as it ensures that all users in the room have a (mostly) consistent view of the state of the room. If the view of the state on different servers diverges it can lead to bifurcation of the room due to e.g. servers disagreeing on who is in the room.

Intuitively, using rejected events feels dangerous, however:

- Servers cannot arbitrarily make up state, since they still need to pass the auth checks based on the event’s auth chain (e.g. they can’t grant themselves power levels if they didn’t have them before).
- For a previously rejected event to pass auth there must be a set of state that allows said event. A malicious server could therefore produce a fork where it claims the state is that particular set of state, duplicate the rejected event to point to that fork, and send the event. The duplicated event would then pass the auth checks. Ignoring rejected events would therefore not eliminate any potential attack vectors.

Rejected auth events are deliberately excluded from use in the iterative auth checks, as auth events aren’t re-authed (although non-auth events are) during the iterative auth checks.