$$ \newcommand \FilterTimeout {\mathrm{FilterTimeout}} \newcommand \DeadlineTimeout {\mathrm{DeadlineTimeout}} \newcommand \Cert {\mathit{cert}} \newcommand \Next {\mathit{next}} $$

New Step

A player may also update its step after receiving a timeout event.

On observing a timeout event of \( \FilterTimeout(p) \) for a period \( p \), the player sets \( s := \Cert \).

On observing a timeout event of \( \DeadlineTimeout(p) \) for a period \( p \), the player sets \( s := \Next_0 \).

On observing a timeout event of \( \DeadlineTimeout(p) + 2^{s_t}\lambda + u \) where \( u \in [0, 2^{s_t}\lambda) \) sampled uniformly at random, the player sets \( s := s_t \).

⚙️ IMPLEMENTATION

New step reference implementation.

In other words,

$$ \begin{aligned} &N((r, p, s, \bar{s}, V, P, \bar{v}), L, t(\FilterTimeout(p), p)) &&= ((r, p, \Cert, \bar{s}, V, P, \bar{v}), L’, \ldots) \\
&N((r, p, s, \bar{s}, V, P, \bar{v}), L, t(\DeadlineTimeout(p), p)) &&= ((r, p, \Next_0, \bar{s}, V, P, \bar{v}), L’, \ldots) \\
&N((r, p, s, \bar{s}, V, P, \bar{v}), L, t(\DeadlineTimeout(p) + 2^{s_t}\lambda + u, p)) &&= ((r, p, \Next_{s_t}, \bar{s}, V, P, \bar{v}), L’, \ldots). \end{aligned} $$