diff --git a/spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md b/spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md index d6fcb54b6..993387ff0 100644 --- a/spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md +++ b/spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md @@ -42,10 +42,10 @@ and drifts of local clocks from real time. #### **[PBTS-CLOCK-PRECISION.0]** There exists a system parameter `PRECISION`, such that -for any two processes `p` and `q`, with local clocks `C_p` and `C_q`: +for any two processes `p` and `q`, with local clocks Cp and Cq: - If `p` and `q` are equipped with synchronized clocks, - then for any real-time `t` we have `|C_p(t) - C_q(t)| <= PRECISION`. + then for any real-time `t` we have |Cp(t) - Cq(t)| <= PRECISION. `PRECISION` thus bounds the difference on the times simultaneously read by processes from their local clocks, so that their clocks can be considered synchronized. @@ -60,12 +60,12 @@ processes from their clocks to real time. For the sake of completeness, we define a parameter `ACCURACY` such that: - At real time `t` there is at least one correct process `p` which clock marks - `C_p(t)` with `|C_p(t) - t| <= ACCURACY`. + Cp(t) with |Cp(t) - t| <= ACCURACY. As a consequence, applying the definition of `PRECISION`, we have: - At real time `t` the synchronized clock of any correct process `p` marks - `C_p(t)` with `|C_p(t) - t| <= ACCURACY + PRECISION`. + Cp(t) with |Cp(t) - t| <= ACCURACY + PRECISION. The reason for not adopting `ACCURACY` as a system parameter is the assumption that `PRECISION >> ACCURACY`. @@ -163,7 +163,7 @@ rounds, but the evaluation of the `timely` predicate is only relevant at round > Considering the algorithm in the [arXiv paper][arXiv], a new proposal is > produced by the `getValue()` method, invoked by the proposer `p` of round -> `round_p` when starting its proposing round with a nil `validValue_p`. +> roundp when starting its proposing round with a nil validValuep. > The first round at which a value `v` is proposed is then the round at which > the proposal for `v` was produced, and broadcast in a `PROPOSAL` message with > `vr = -1`. @@ -190,7 +190,7 @@ associated proposal time `v.time` is considered `timely`. > Considering the algorithm in the [arXiv paper][arXiv], the `timely` predicate > is evaluated by a process `p` when it receives a valid `PROPOSAL` message -> from the proposer of the current round `round_p` with `vr = -1`. +> from the proposer of the current round roundp with `vr = -1`. ### Timely Proof-of-Locks @@ -259,7 +259,7 @@ produced (by hypothesis) we can affirm that at least one correct process (also) observed a `POL(v,vr)`. > Considering the algorithm in the [arXiv paper][arXiv], `v` was proposed by -> the proposer `p` of round `round_p` because its `validValue_p` variable was +> the proposer `p` of round roundp because its validValuep variable was > set to `v`. > The `PROPOSAL` message broadcast by the proposer, in this case, had `vr > -1`, > and it could only be accepted by processes that also observed a `POL(v,vr)`.