$$ \newcommand \PSfunction {\textbf{function }} \newcommand \PSreturn {\textbf{return }} \newcommand \PSendfunction {\textbf{end function}} \newcommand \PSswitch {\textbf{switch }} \newcommand \PScase {\textbf{case }} \newcommand \PSdefault {\textbf{default}} \newcommand \PSendswitch {\textbf{end switch}} \newcommand \PSfor {\textbf{for }} \newcommand \PSendfor {\textbf{end for}} \newcommand \PSwhile {\textbf{while }} \newcommand \PSendwhile {\textbf{end while}} \newcommand \PSdo {\textbf{ do}} \newcommand \PSif {\textbf{if }} \newcommand \PSelseif {\textbf{else if }} \newcommand \PSelse {\textbf{else}} \newcommand \PSthen {\textbf{ then}} \newcommand \PSendif {\textbf{end if}} \newcommand \PSnot {\textbf{not }} \newcommand \PScomment {\qquad \small \textsf} $$

$$ \newcommand \DeadlineTimeout {\mathrm{DeadlineTimeout}} \newcommand \Recovery {\mathrm{Recovery}} \newcommand \ResynchronizationAttempt {\mathrm{ResynchronizationAttempt}} \newcommand \Sortition {\mathrm{Sortition}} \newcommand \Proposal {\mathrm{Proposal}} \newcommand \IsCommittable {\mathrm{IsCommittable}} \newcommand \Broadcast {\mathrm{Broadcast}} \newcommand \Vote {\mathrm{Vote}} \newcommand \Bundle {\mathrm{Bundle}} \newcommand \Cert {\mathit{cert}} \newcommand \Next {\mathit{next}} \newcommand \c {\mathit{credentials}} \newcommand \prop {\mathit{proposal}} \newcommand \s {\mathit{step}} $$

Recovery

The recovery algorithm is executed periodically, whenever a \( \Bundle_\Cert \) has not been observed before \( \DeadlineTimeout(p) \) for a given period \( p \).

Algorithm

\( \textbf{Algorithm 9} \text{: Recovery} \)

$$ \begin{aligned} &\text{1: } \PSfunction \Recovery() \\ &\text{2: } \quad \ResynchronizationAttempt() \\ &\text{3: } \quad \PSfor a \in A \PSdo \\ &\text{4: } \quad \quad \c \gets \Sortition(a_I, r, p, s) \\ &\text{5: } \quad \quad \PSif \c_j > 0 \PSthen \\ &\text{6: } \quad \quad \quad \PSif \exists v = \Proposal_v(\prop, \prop_p, \prop_I) \\ &\text{ } \quad \quad \quad \quad \quad \text{for some } \prop \in P \mid \IsCommittable(v) \PSthen \\ &\text{7: } \quad \quad \quad \quad \Broadcast(\Vote(a_I, r, p, s, v, \c)) \\ &\text{8: } \quad \quad \quad \PSelseif \exists s_0 > \Cert \mid \Bundle(r, p - 1, s_0, \bot) \subseteq V \land \\ &\text{ } \quad \quad \quad \quad \quad \quad \quad \exists s_1 > \Cert \mid \Bundle(r, p - 1, s_1, \bar{v}) \subseteq V \PSthen \\ &\text{9: } \quad \quad \quad \quad \Broadcast(\Vote(a_I, r, p, s, \bar{v}, \c)) \\ &\text{10:} \quad \quad \quad \PSelse \\ &\text{11:} \quad \quad \quad \quad \Broadcast(\Vote(a_I, r, p, s, \bot, \c)) \\ &\text{12:} \quad \quad \quad \PSendif \\ &\text{13:} \quad \quad \PSendif \\ &\text{14:} \quad \PSendfor \\ &\text{15:} \quad \s \gets \s + 1 \\ &\text{16: } \PSendfunction \end{aligned} $$

⚙️ IMPLEMENTATION

Next vote issuance reference implementation.

The node starts by making a resynchronization attempt (Line 2).

Afterward (Lines 3:5), the node plays independently for each online account (registered on the node). This means that for every account available in \( A \), the \( \Sortition \) algorithm is run, and accounts selected in the recovery committee (i.e., the players) for the current step \( \Next_k \) (that is, those whose \( \c_j > 0 \)) will produce one of the following three distinct outputs (Lines 6:14):

• If a proposal-value \( v \) can be committed in the current context, then the player broadcasts a \( \Next_k \) vote for \( v \).

• If no proposal-value can be committed, and

  • No recovery step \( \Bundle \) for the empty proposal-value (\( \bot \)) was observed in the previous period, and
  • A recovery step \( \Bundle \) for the pinned value was observed in the previous period¹,

  then a \( \Next_k \) vote for \( \bar{v} \) is broadcast by the player.

• Finally, if none of the above conditions were met, a \( \Next_k \) vote for \( \bot \) is broadcast.

A player is forbidden from equivocating in \( \Next_k \) votes.

Lastly (Line 15), the node’s current \( \s \) is updated.

For a formal definition of this functionality, refer to the ABFT normative section.

1. This implies \( \bar{v} \neq \bot \). ↩