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

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 a dagger (†) 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 \( \Vote_k \in V \).

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

• Ignores it if \( s_k > 0 \) 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
    • \( s_k \in (\Next_0, \Late) \)

  • \( r_k = r \) 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
    • \( p > 0 \) and \( p_k = p - 1 \) and \( s_k \in (\Next_0, \Late) \) and \( s_k \notin [\bar{s}-1,\bar{s}+1] \).

• MAY ignore it if \( s_k = 0 \) and its credential does not have higher priority than that of every proposal-vote accepted or relayed for \( (r_k, p_k) \).

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

A player MAY also relay a verified proposal-vote with \( r_k < r \) and \( p_k = s_k = 0 \), without observing it, if its credential has higher priority than that of every proposal-vote accepted or relayed for \( (r_k, 0) \).

Note

The reference implementation does so within a bounded window of past rounds, supporting the adaptive filter timeout described in the non-normative section.

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

$$ N(S, L, \Vote_k(r_k, p_k, s_k, v)) = (S’ \cup \{\Vote_k(r_k, p_k, s_k, v)\}, L’, (\Vote_k^\ast(r_k, p_k, s_k, v),\ldots)); $$

and if a player relays the vote without observing it, then

$$ N(S, L, \Vote_k(r_k, p_k, s_k, v)) = (S, L, (\Vote_k^\ast(r_k, p_k, s_k, v))). $$

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
  • \( s_k \neq \Cert \) and \( p_k + 1 < p \).

• Otherwise, verifies and 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 \( \Bundle(r_k, p_k, s_k, v’) \), then the player relays it and executes any consequent action; otherwise, 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

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

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

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

Proposals

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

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

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

• Relays \( \Proposal(v) \) if \( v = \bar{v} \), \( v = \rho(S, r, q) \) for \( q \in \{p-1, p, p+1\} \) when not \( \bot \), or \( v = \rho(S, r+1, 0) \).

• Otherwise, ignores it.

A relayed proposal is observed and produces any consequent output only if it is valid.

When relaying \( \Proposal(v) \), the player SHOULD attach an accepted current-period proposal-vote for \( v \) as authenticator, when available.

Specifically, if the player ignores a proposal, then

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

while if a player relays a valid proposal, then

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

If a relayed proposal is invalid, it is not observed:

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

Note

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

• \( \bar{v} \),

• \( \rho(S, r, q) \) for \( q \in \{p-1, p, p+1\} \) when not \( \bot \),

• \( \rho(S, r+1, 0) \).