$$ \newcommand \MaxVersionStringLen {V_{\max}} \newcommand \DefaultUpgradeWaitRounds {\delta_x} \newcommand \MaxUpgradeWaitRounds {\delta_{x_{\max}}} \newcommand \MinUpgradeWaitRounds {\delta_{x_{\min}}} \newcommand \UpgradeThreshold {\tau} \newcommand \UpgradeVoteRounds {\delta_d} $$

Protocol Upgrade State

A protocol version \( v \) is a string no more than \( \MaxVersionStringLen \) bytes long. It corresponds to parameters used to execute some version of the Algorand protocol.

The upgrade vote in each block consists of:

• A protocol version \( v_r \);
• A 64-bit unsigned integer \( x_r \) which indicates the delay between the acceptance of a protocol version and its execution;
• A single bit \( b \) indicating whether the block proposer supports the given protocol version.

The upgrade state in each block/state consists of:

• The current protocol version \( v_r^{\ast} \);
• The next proposed protocol version \( v_r^{\prime} \);
• A 64-bit round number \( s_r \) counting the number of votes for the next protocol version;
• A 64-bit round number \( d_r \) specifying the deadline for voting on the next protocol version;
• A 64-bit round number \( x_r^{\prime} \) specifying when the next proposed protocol version would take effect, if passed.

An upgrade vote \( (v_r, x_r, b) \) is valid given the upgrade state \( (v_r^{\ast}, v_r^{\prime}, s_r, d_r, x_r^{\prime}) \) if \( v_r \) is the empty string or \( v_r^{\prime} \) is the empty string, \( \MinUpgradeWaitRounds \leq x_r \leq \MaxUpgradeWaitRounds \), and either:

• \( b = 0 \) or
• \( b = 1 \) with \( r < d_r \) and either
  • \( v_r^{\prime} \) is not the empty string or
  • \( v_r \) is not the empty string.

If the vote is valid, then the new upgrade state is

$$ (v_{r+1}^{\ast}, v_{r+1}^{\prime}, s_{r+1}, d_{r+1}, x_{r+1}) $$

Where

• \( v_{r+1}^{\ast} \) is \( v_r^{\prime} \) if \( r = x_r^{\prime} \) and \( v_r^{\ast} \) otherwise.

• \( v^{\prime}_{r+1} \) is

  • the empty string if \( r = x_r^{\prime} \) or both \( r = s_r \) and \( s_r + b < \UpgradeThreshold \),
  • \( v_r \) if \( v_r^{\prime} \) is the empty string, and
  • \( v_r^{\prime} \) otherwise.

• \( s_{r+1} \) is

  • \( 0 \) if \( r = x_r^{\prime} \) or both \( r = s_r \) and \( s_r + b < \UpgradeThreshold \), and
  • \( s_r + b \) otherwise

• \( d_{r+1} \) is

  • \( 0 \) if \( r = x_r^{\prime} \) or both \( r = s_r \) and \( s_r + b < \UpgradeThreshold \),
  • \( r + \UpgradeVoteRounds \) if \( v_r^{\prime} \) is the empty string and \( v_r \) is not the empty string, and
  • \( d_r \) otherwise.

• \( x_{r+1} \) is

  • \( 0 \) if \( r = x_r^{\prime} \) or both \( r = s_r \) and \( s_r + b < \UpgradeThreshold \),
  • \( r + \UpgradeVoteRounds + \delta \) if \( v_r^{\prime} \) is the empty string and \( v_r \) is not the empty string (where \( \delta = \DefaultUpgradeWaitRounds \) if \( x_r = 0 \) and \( \delta = x_r \) if \( x_r \neq 0 \)), and
  • \( x_r^{\prime} \) otherwise.