$$ \newcommand \Vote {\mathrm{Vote}} \newcommand \Late {\mathit{late}} \newcommand \Down {\mathit{down}} \newcommand \Next {\mathit{next}} \newcommand \Bundle {\mathrm{Bundle}} \newcommand \Proposal {\mathrm{Proposal}} $$

Relay Rules

Here we describe how players handle message events.

Whenever the player receives a message event, it may decide to relay that or another message. In this case, the player will produce that output before producing any subsequent output (which may result from the player’s observation of that message; see the broadcast rules below).

A player may receive messages from a misbehaving peer. These cases are marked with an asterisk (*) and enable the node to perform a special action (e.g., disconnect from the peer).

Note

For examples of what these special actions may involve, see the Algorand Network non-normative section.

We say that a player ignores a message if it produces no outputs on receiving that message.

Votes

On receiving a vote \( \Vote_k(r_k, p_k, s_k, v) \) a player

• Ignores* it if \( \Vote_k \) is malformed or trivially invalid.

• Ignores it if \( s = 0 \) and \( \Vote_k \in V \).

• Ignores it if \( s = 0 \) and \( \Vote_k \) is an equivocation.

• Ignores it if \( s > 0 \) and \( \Vote_k \) is a second equivocation.

• Ignores it if

  • \( r_k \notin [r,r+1] \) or

  • \( r_k = r + 1 \) and either

    • \( p_k > 0 \) or
    • \( s_k \in (\Next_0, \Late) \) or

  • \( r_k = r \) and one of

    • \( p_k \notin [p-1,p+1] \) or
    • \( p_k = p + 1 \) and \( s_k \in (\Next_0, \Late) \) or
    • \( p_k = p \) and \( s_k \in (\Next_0, \Late) \) and \( s_k \notin [s-1,s+1] \) or
    • \( p_k = p - 1 \) and \( s_k \in (\Next_0, \Late) \) and \( s_k \notin [\bar{s}-1,\bar{s}+1] \).

• Otherwise, relays \( \Vote_k \), observes it, and then produces any consequent output.

Specifically, if a player ignores the vote, then

$$ N(S, L, \Vote_k(r_k, p_k, s_k, v)) = (S, L, \epsilon) $$

while if a player relays the vote, then

$$ N(S, L, \Vote_k(r_k, p_k, s_k, v)) = (S’ \cup \Vote(I, r_k, p_k, s_k, v), L’, (\Vote_k^\ast(r_k, p_k, s_k, v),\ldots)). $$

Bundles

On receiving a bundle \( \Bundle(r_k, p_k, s_k, v) \) a player

• Ignores* it if \( Bundle(r_k, p_k, s_k, v) \) is malformed or trivially invalid.

• Ignores it if

  • \( r_k \neq r \) or
  • \( r_k = r \) and \( p_k + 1 < p \).

• Otherwise, observes the votes in \( \Bundle(r_k, p_k, s_k, v) \) in sequence. If there exists a vote that causes the player to observe some bundle \( \Bundle(r_k, p_k, s_k, v’) \) for some \( s_k \), then the player relays \( \Bundle(r_k, p_k, s_k, v’) \), and then executes any consequent action; if there does not, the player ignores it.

Specifically, if the player ignores the bundle without observing its votes, then

$$ N(S, L, \Bundle(r_k, p_k, s_k, v)) = (S, L, \epsilon); $$

while if a player ignores the bundle but observes its votes, then

$$ N(S, L, \Bundle(r_k, p_k, s_k, v)) = (S’ \cup \Bundle(r_k, p_k, s_k, v), L, \epsilon); $$

and if a player, on observing the votes in the bundle, observes a bundle for some value (not necessarily distinct from the bundle’s value), then

$$ N(S, L, \Bundle(r_k, p_k, s_k, v)) = (S’ \cup \Bundle(r_k, p_k, s_k, v), L’, (\Bundle^\ast(r_k, p_k, s_k, v’), \ldots)). $$

Proposals

On receiving a proposal \( \Proposal(v) \) a player

• Relays \( \Proposal(v) \) if \( \sigma(S, r+1, 0) = v \).

• Ignores* it if it is malformed or trivially invalid.

• Ignores it if \( \Proposal(v) \in P \).

• Relays \( \Proposal(v) \), observes it, and then produces any consequent output, if \( v \in \{\sigma(S, r, p), \bar{v}, \mu(S, r, p)\} \).

• Otherwise, ignores it.

Specifically, if the player ignores a proposal, then

$$ N(S, L, \Proposal(v)) = (S, L, \epsilon) $$

while if a player relays the proposal after checking if it is valid, then

$$ N(S, L, \Proposal(v)) = (S’ \cup \Proposal(v), L’, (\Proposal^\ast(v), \ldots)). $$

However, in the first condition above, the player relays \( \Proposal(v) \) without checking if it is valid.

Since the proposal has not been seen to be valid, the player cannot observe it yet, so

$$ N(S, L, \Proposal(v)) = (S, L, (\Proposal^\ast(v))). $$

Note

An implementation may buffer a proposal in this case. Specifically, an implementation which relays a proposal without checking that it is valid, may optionally choose to replay this event when it observes that a new round has begun (see State Transition section). In this case, at the conclusion of a new round, this proposal is processed once again as input.

Implementations MAY store and relay fewer proposals than specified here to improve efficiency. However, implementations MUST relay proposals which match the following proposal-values (where \( r \) is the current round and \( p \) is the current period):

• \( \bar{v} \),

• \( \sigma(S, r, p), \sigma(S, r, p-1) \),

• \( \mu(S, r, p) \) if \( \sigma(S, r, p) \) is not set and \( \mu(S, r, p+1) \) if \( \sigma(S, r, p+1) \) is not set.