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PBTS: system model made more precise (#8096)

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* PBTS model: precision, accuracy, and delay defs

* PBTS model: consensus properties reviewed

* PBTS model: reinforcing alignment with UTC

* PBTS model: precision parameter embodies accuracy

* PBTS model: discussion about accuracy shortened

* PBTS model: proposal time monotonocity rephrased

* PBTS model: precision, accuracy, and delay defs

* PBTS model: consensus properties reviewed

* PBTS model: reinforcing alignment with UTC

* PBTS model: precision parameter embodies accuracy

* PBTS model: discussion about accuracy shortened

* PBTS model: proposal time monotonocity rephrased

* PBTS model: Safety Invariants subsection

* PBTS model: MSGDELAY description shortened

* PBTS model: timely proposals definition refined

* PBTS model: some formatting changes

* PBTS model: timely predicate definition

* PBTS model: timely proof-of-lock re-defined

* PBTS model: derived proof-of-lock requirements

   * The property needs to be properly demonstrated.

* Apply suggestions from William

Co-authored-by: William Banfield <4561443+williambanfield@users.noreply.github.com>

* PBTS model: reference to arXiv algorithm on timely

* PBTS model: typos fixed

* PBTS model: derived POL "demonstration"

* PBTS model: fix formatting, r' renamed to vr

* PBTS model: minor fixes

* PBTS model: derived POL proof ammended

* PBTS safety: consensus validity with time inequalty

* PBTS: renamed receiveTime to proposalReceptionTime

* PBTS safety: short intro, some links

* PBTS model: safety refactored again

* PBTS model: liveness condition stated

* PBTS liveness: minor change

* Update spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md

Co-authored-by: William Banfield <4561443+williambanfield@users.noreply.github.com>

* Update spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md

Co-authored-by: William Banfield <4561443+williambanfield@users.noreply.github.com>

* Update spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md

* Update spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md

Co-authored-by: Josef Widder <44643235+josef-widder@users.noreply.github.com>

* Update spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md

Co-authored-by: Josef Widder <44643235+josef-widder@users.noreply.github.com>

* Update spec/consensus/proposer-based-timestamp/pbts-sysmodel_002_draft.md

Co-authored-by: Josef Widder <44643235+josef-widder@users.noreply.github.com>

* PBTS sysmodel: formmatting typo fixed

Co-authored-by: William Banfield <4561443+williambanfield@users.noreply.github.com>
Co-authored-by: Josef Widder <44643235+josef-widder@users.noreply.github.com>
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@@ -1,16 +1,31 @@
# PBTS: System Model and Properties
## Outline
- [System model](#system-model)
- [Synchronized clocks](#synchronized-clocks)
- [Message delays](#message-delays)
- [Problem Statement](#problem-statement)
- [Protocol Analysis - Timely Proposals](#protocol-analysis---timely-proposals)
- [Timely Proof-of-Locks](#timely-proof-of-locks)
- [Derived Proof-of-Locks](#derived-proof-of-locks)
- [Temporal Analysis](#temporal-analysis)
- [Safety](#safety)
- [Liveness](#liveness)
## System Model
#### **[PBTS-CLOCK-NEWTON.0]**
There is a reference Newtonian real-time `t` (UTC).
There is a reference Newtonian real-time `t`.
No process has direct access to this reference time, used only for specification purposes.
The reference real-time is assumed to be aligned with the Coordinated Universal Time (UTC).
### Synchronized clocks
Processes are assumed to be equipped with synchronized clocks.
Processes are assumed to be equipped with synchronized clocks,
aligned with the Coordinated Universal Time (UTC).
This requires processes to periodically synchronize their local clocks with an
external and trusted source of the time (e.g. NTP servers).
@@ -27,43 +42,35 @@ 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`,
that read their local clocks at the same real-time `t`, we have:
for any two processes `p` and `q`, with local clocks `C_p` and `C_q`:
- If `p` and `q` are equipped with synchronized clocks, then `|C_p(t) - C_q(t)| < PRECISION`
- If `p` and `q` are equipped with synchronized clocks,
then for any real-time `t` we have `|C_p(t) - C_q(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.
#### Accuracy
The [first draft][sysmodel_v1] of this specification included a second clock-related parameter, `ACCURACY`,
that relates the values read by processes from their synchronized clocks with real time:
A second relevant clock parameter is accuracy, which binds the values read by
processes from their clocks to real time.
- If `p` is a process is equipped with a synchronized clock, then at real time
`t` it reads from its clock time `C_p(t)` with `|C_p(t) - t| < ACCURACY`
##### **[PBTS-CLOCK-ACCURACY.0]**
The adoption of `ACCURACY` as the upper bound on the difference between clock
readings and real time, however, renders the `PRECISION` parameter redundant.
In fact, if we assume that clocks readings are at most `ACCURACY` from real
time, we would therefore be assuming that they cannot be more than `2 * ACCURACY`
apart from each other, thus establishing a worst-case upper bound for `PRECISION`.
The approach we take is to assume that processes clocks are periodically
synchronized with an external source of time, thus improving their accuracy.
This allows us to adopt a relaxed version of the above `ACCURACY` definition:
##### **[PBTS-CLOCK-FAIR.0]**
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`
`C_p(t)` with `|C_p(t) - t| <= ACCURACY`.
Then, through [PBTS-CLOCK-PRECISION] we can extend this relation of clock times
with real time to every correct process, which will have a clock with accuracy
bound by `ACCURACY + PRECISION`.
But, for the sake of simpler specification we can assume that the `PRECISION`,
which is a worst-case parameter that applies to all correct processes,
includes the best `ACCURACY` achieved by any of them.
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`.
The reason for not adopting `ACCURACY` as a system parameter is the assumption
that `PRECISION >> ACCURACY`.
This allows us to consider, for practical purposes, that the `PRECISION` system
parameter embodies the `ACCURACY` model parameter.
### Message Delays
@@ -79,172 +86,264 @@ defining a lower bound, a *minimum time* that a correct process assigns to propo
While *minimum delay* for delivering a proposal to a destination allows defining
an upper bound, the *maximum time* assigned to a proposal.
#### **[PBTS-MSG-D.0]**
#### **[PBTS-MSG-DELAY.0]**
There exists a system parameter `MSGDELAY` for end-to-end delays of messages carrying proposals,
such for any two correct processes `p` and `q`, and any real time `t`:
There exists a system parameter `MSGDELAY` for end-to-end delays of proposal messages,
such for any two correct processes `p` and `q`:
- If `p` sends a message `m` carrying a proposal at time `ts`,
then if `q` receives the message and learns the proposal,
`q` does that at time `t` such that `ts <= t <= ts + MSGDELAY`.
- If `p` sends a proposal message `m` at real time `t` and `q` receives `m` at
real time `t'`, then `t <= t' <= t + MSGDELAY`.
While we don't want to impose particular restrictions regarding the format of `m`,
we need to assume that their size is upper bounded.
In practice, using messages with a fixed-size to carry proposals allows
for a more accurate estimation of `MSGDELAY`, and therefore is advised.
Notice that, as a system parameter, `MSGDELAY` should be observed for any
proposal message broadcast by correct processes: it is a *worst-case* parameter.
As message delays depends on the message size, the above requirement implicitly
indicates that the size of proposal messages is either fixed or upper bounded.
## Problem Statement
In this section we define the properties of Tendermint consensus
(cf. the [arXiv paper][arXiv]) in this new system model.
(cf. the [arXiv paper][arXiv]) in this system model.
#### **[PBTS-PROPOSE.0]**
### **[PBTS-PROPOSE.0]**
A proposer proposes a consensus value `v` with an associated proposal time `v.time`.
A proposer proposes a consensus value `v` that includes a proposal time
`v.time`.
> We then restrict the allowed decisions along the following lines:
#### **[PBTS-INV-AGREEMENT.0]**
[Agreement] No two correct processes decide on different values `v`. (This implies that no two correct processes decide on different proposal times `v.time`.)
- [Agreement] No two correct processes decide on different values `v`.
This implies that no two correct processes decide on different proposal times
`v.time`.
#### **[PBTS-INV-VALID.0]**
[Validity] If a correct process decides on value `v`,
then `v` satisfies a predefined `valid` predicate.
- [Validity] If a correct process decides on value `v`, then `v` satisfies a
predefined `valid` predicate.
With respect to PBTS, the `valid` predicate requires proposal times to be
[monotonic](./pbts-algorithm_002_draft.md#time-monotonicity) over heights of
consensus:
##### **[PBTS-INV-MONOTONICITY.0]**
- If a correct process decides on value `v` at the height `h` of consensus,
thus setting `decision[h] = v`, then `v.time > decision[h'].time` for all
previous heights `h' < h`.
The monotonicity of proposal times, and external validity in general,
implicitly assumes that heights of consensus are executed in order.
#### **[PBTS-INV-TIMELY.0]**
[Time-Validity] If a correct process decides on value `v`,
then the associated proposal time `v.time` satisfies a predefined `timely` predicate.
- [Time-Validity] If a correct process decides on value `v`, then the proposal
time `v.time` was considered `timely` by at least one correct process.
> Both [Validity] and [Time-Validity] must be observed even if up to `2f` validators are faulty.
PBTS introduces a `timely` predicate that restricts the allowed decisions based
on the proposal time `v.time` associated with a proposed value `v`.
As a synchronous predicate, the time at which it is evaluated impacts on
whether a process accepts or reject a proposal time.
For this reason, the Time-Validity property refers to the previous evaluation
of the `timely` predicate, detailed in the following section.
### Timely proposals
## Protocol Analysis - Timely proposals
For PBTS, a `proposal` is a tuple `(v, v.time, v.round)`, where:
- `v` is the proposed value;
- `v.time` is the associated proposal time;
- `v.round` is the round at which `v` was first proposed.
We include the proposal round `v.round` in the proposal definition because a
value `v` and its associated proposal time `v.time` can be proposed in multiple
rounds, but the evaluation of the `timely` predicate is only relevant at round
`v.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`.
> 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`.
#### **[PBTS-PROPOSAL-RECEPTION.0]**
The `timely` predicate is evaluated when a process receives a proposal.
Let `now_p` be time a process `p` reads from its local clock when `p` receives a proposal.
Let `v` be the proposed value and `v.time` the proposal time.
The proposal is considered `timely` by `p` if:
More precisely, let `p` be a correct process:
#### **[PBTS-RECEPTION-STEP.1]**
- `proposalReceptionTime(p,r)` is the time `p` reads from its local clock when
`p` is at round `r` and receives the proposal of round `r`.
1. `now_p >= v.time - PRECISION` and
1. `now_p <= v.time + MSGDELAY + PRECISION`
#### **[PBTS-TIMELY.0]**
The proposal `(v, v.time, v.round)` is considered `timely` by a correct process
`p` if:
1. `proposalReceptionTime(p,v.round)` is set, and
1. `proposalReceptionTime(p,v.round) >= v.time - PRECISION`, and
1. `proposalReceptionTime(p,v.round) <= v.time + MSGDELAY + PRECISION`.
A correct process at round `v.round` only sends a `PREVOTE` for `v` if the
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`.
### Timely Proof-of-Locks
We denote by `POL(v,r)` a *Proof-of-Lock* of value `v` at the round `r` of consensus.
`POL(v,r)` consists of a set of `PREVOTE` messages of round `r` for the value `v`
from processes whose cumulative voting power is at least `2f + 1`.
A *Proof-of-Lock* is a set of `PREVOTE` messages of round of consensus for the
same value from processes whose cumulative voting power is at least `2f + 1`.
We denote as `POL(v,r)` a proof-of-lock of value `v` at round `r`.
#### **[PBTS-TIMELY-POL.1]**
For PBTS, we are particularly interested in the `POL(v,v.round)` produced in
the round `v.round` at which a value `v` was first proposed.
We call it a *timely* proof-of-lock for `v` because it can only be observed
if at least one correct process considered it `timely`:
#### **[PBTS-TIMELY-POL.0]**
If
- there is a valid `POL(v,r*)` for height `h`, and
- `r*` is the lowest-numbered round `r` of height `h` for which there is a valid `POL(v,r)`, and
- `POL(v,r*)` contains a `PREVOTE` message from at least one correct process,
- there is a valid `POL(v,r)` with `r = v.round`, and
- `POL(v,v.round)` contains a `PREVOTE` message from at least one correct process,
Then, where `p` is a such correct process:
Then, let `p` is a such correct process:
- `p` received a `PROPOSE` message of round `r*` and height `h`, and
- the `PROPOSE` message contained a proposal for value `v` with proposal time `v.time`, and
- a correct process `p` considered the proposal `timely`.
- `p` received a `PROPOSAL` message of round `v.round`, and
- the `PROPOSAL` message contained a proposal `(v, v.time, v.round)`, and
- `p` was in round `v.round` and evaluated the proposal time `v.time` as `timely`.
The round `r*` above defined will be, in most cases,
the round in which `v` was originally proposed, and when `v.time` was assigned,
using a `PROPOSE` message with `POLRound = -1`.
In any case, at least one correct process must consider the proposal `timely` at round `r*`
to enable a valid `POL(v,r*)` to be observed.
The existence of a such correct process `p` is guaranteed provided that the
voting power of Byzantine processes is bounded by `2f`.
### Derived Proof-of-Locks
#### **[PBTS-DERIVED-POL.1]**
The existence of `POL(v,r)` is a requirement for the decision of `v` at round
`r` of consensus.
At the same time, the Time-Validity property establishes that if `v` is decided
then a timely proof-of-lock `POL(v,v.round)` must have been produced.
So, we need to demonstrate here that any valid `POL(v,r)` is either a timely
proof-of-lock or it is derived from a timely proof-of-lock:
#### **[PBTS-DERIVED-POL.0]**
If
- there is a valid `POL(v,r)` for height `h`, and
- there is a valid `POL(v,r)`, and
- `POL(v,r)` contains a `PREVOTE` message from at least one correct process,
Then
- there is a valid `POL(v,r*)` for height `h`, with `r* <= r`, and
- `POL(v,r*)` contains a `PREVOTE` message from at least one correct process, and
- a correct process considered the proposal for `v` `timely` at round `r*`.
- there is a valid `POL(v,v.round)` with `v.round <= r` which is a timely proof-of-lock.
The above relation derives from a recursion on the round number `r`.
It is trivially observed when `r = r*`, the base of the recursion,
when a timely `POL(v,r*)` is obtained.
We need to ensure that, once a timely `POL(v,r*)` is obtained,
it is possible to obtain a valid `POL(v,r)` with `r > r*`,
without the need of satisfying the `timely` predicate (again) in round `r`.
In fact, since rounds are started in order, it is not likely that
a proposal time `v.time`, assigned at round `r*`,
will still be considered `timely` when the round `r > r*` is in progress.
The above relation is trivially observed when `r = v.round`, as `POL(v,r)` must
be a timely proof-of-lock.
Notice that we cannot have `r < v.round`, as `v.round` is defined as the first
round at which `v` was proposed.
In other words, the algorithm should ensure that once a `POL(v,r*)` attests
that the proposal for `v` is `timely`,
further valid `POL(v,r)` with `r > r*` can be obtained,
even though processes do not consider the proposal for `v` `timely` any longer.
For `r > v.round` we need to demonstrate that if there is a valid `POL(v,r)`,
then a timely `POL(v,v.round)` was previously obtained.
We observe that a condition for observing a `POL(v,r)` is that the proposer of
round `r` has broadcast a `PROPOSAL` message for `v`.
As `r > v.round`, we can affirm that `v` was not produced in round `r`.
Instead, by the protocol operation, `v` was a *valid value* for the proposer of
round `r`, which means that if the proposer has observed a `POL(v,vr)` with `vr
< r`.
The above operation considers a *correct* proposer, but since a `POL(v,r)` was
produced (by hypothesis) we can affirm that at least one correct process (also)
observed a `POL(v,vr)`.
> This can be achieved if the proposer of round `r' > r*` proposes `v` in a `PROPOSE` message
with `POLRound = r*`, and at least one correct processes is aware of a `POL(v,r*)`.
> From this point, if a valid `POL(v,r')` is achieved, it can replace the adopted `POL(v,r*)`.
> 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
> 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)`.
### SAFETY
Thus, if there is a `POL(v,r)` with `r > v.round`, then there is a valid
`POL(v,vr)` with `v.round <= vr < r`.
If `vr = v.round` then `POL(vr,v)` is a timely proof-of-lock and we are done.
Otherwise, there is another valid `POL(v,vr')` with `v.round <= vr' < vr`,
and the above reasoning can be recursively applied until we get `vr' = v.round`
and observe a timely proof-of-lock.
The safety of the algorithm requires a *timely* proof-of-lock for a decided value,
either directly evaluated by a correct process,
or indirectly received through a derived proof-of-lock.
## Temporal analysis
#### **[PBTS-CONSENSUS-TIME-VALID.0]**
In this section we present invariants that need be observed for ensuring that
PBTS is both safe and live.
In addition to the variables and system parameters already defined, we use
`beginRound(p,r)` as the value of process `p`'s local clock
when it starts round `r` of consensus.
### Safety
The safety of PBTS requires that if a value `v` is decided, then at least one
correct process `p` considered the associated proposal time `v.time` timely.
Following the definition of [timely proposals](#pbts-timely0) and
proof-of-locks, we require this condition to be asserted at a specific round of
consensus, defined as `v.round`:
#### **[PBTS-SAFETY.0]**
If
- there is a valid commit `C` for height `k` and round `r`, and
- there is a valid commit `C` for a value `v`
- `C` contains a `PRECOMMIT` message from at least one correct process
Then, where `p` is one such correct process:
then there is a correct process `p` (not necessarily the same above considered) such that:
- since `p` is correct, `p` received a valid `POL(v,r)`, and
- `POL(v,r)` contains a `PREVOTE` message from at least one correct process, and
- `POL(v,r)` is derived from a timely `POL(v,r*)` with `r* <= r`, and
- `POL(v,r*)` contains a `PREVOTE` message from at least one correct process, and
- a correct process considered a proposal for `v` `timely` at round `r*`.
- `beginRound(p,v.round) <= proposalReceptionTime(p,v.round) <= beginRound(p,v.round+1)` and
- `proposalReceptionTime (p,v.round) - MSGDELAY - PRECISION <= v.time <= proposalReceptionTime(p,v.round) + PRECISION`
### LIVENESS
That is, a correct process `p` started round `v.round` and, while still at
round `v.round`, received a `PROPOSAL` message from round `v.round` proposing
`v`.
Moreover, the reception time of the original proposal for `v`, according with
`p`'s local clock, enabled `p` to consider the proposal time `v.time` as
`timely`.
This is the requirement established by PBTS for issuing a `PREVOTE` for the
proposal `(v, v.time, v.round)`, so for the eventual decision of `v`.
In terms of liveness, we need to ensure that a proposal broadcast by a correct process
will be considered `timely` by any correct process that is ready to accept that proposal.
So, if:
### Liveness
- the proposer `p` of a round `r` is correct,
- there is no `POL(v',r')` for any value `v'` and any round `r' < r`,
- `p` proposes a valid value `v` and sets `v.time` to the time it reads from its local clock,
The liveness of PBTS relies on correct processes accepting proposal times
assigned by correct proposers.
We thus present a set of conditions for assigning a proposal time `v.time` so
that every correct process should be able to issue a `PREVOTE` for `v`.
Then let `q` be a correct process that receives `p`'s proposal, we have:
#### **[PBTS-LIVENESS.0]**
- `q` receives `p`'s proposal after its clock reads `v.time - PRECISION`, and
- if `q` is at or joins round `r` while `p`'s proposal is being transmitted,
then `q` receives `p`'s proposal before its clock reads `v.time + MSGDELAY + PRECISION`
If
> Note that, before `GST`, we cannot ensure that every correct process receives `p`'s proposals, nor that it does it while ready to accept a round `r` proposal.
- the proposer of a round `r` of consensus is correct
- and it proposes a value `v` for the first time, with associated proposal time `v.time`
A correct process `q` as above defined must then consider `p`'s proposal `timely`.
It will then broadcast a `PREVOTE` message for `v` at round `r`,
thus enabling, from the Time-Validity point of view, `v` to be eventually decided.
then the proposal `(v, v.time, r)` is accepted by every correct process provided that:
#### Under-estimated `MSGDELAY`s
- `min{p is correct : beginRound(p,r)} <= v.time <= max{p is correct : beginRound(p,r)}` and
- `max{p is correct : beginRound(p,r)} <= v.time + MSGDELAY + PRECISION <= min{p is correct : beginRound(p,r+1)}`
The liveness assumptions of PBTS are conditioned by a conservative and clever
choice of the timing parameters, specially of `MSGDELAY`.
In fact, if the transmission delay for a message carrying a proposal is wrongly
estimated, correct processes may never consider a valid proposal as `timely`.
The first condition establishes a range of safe proposal times `v.time` for round `r`.
This condition is trivially observed if a correct proposer `p` sets `v.time` to the time it
reads from its clock when starting round `r` and proposing `v`.
A `PROPOSAL` message sent by `p` at local time `v.time` should not be received
by any correct process before its local clock reads `v.time - PRECISION`, so
that condition 2 of [PBTS-TIMELY.0] is observed.
To circumvent this liveness issue, which could result from a misconfiguration,
we assume that the `MSGDELAY` parameter can be increased as rounds do not
succeed on deciding a value, possibly because no proposal is considered
`timely` by enough processes.
The precise behavior for this workaround is under [discussion](https://github.com/tendermint/spec/issues/371).
The second condition establishes that every correct process should start round
`v.round` at a local time that allows `v.time` to still be considered timely,
according to condition 3. of [PBTS-TIMELY.0].
In addition, it requires correct processes to stay long enough in round
`v.round` so that they can receive the `PROPOSAL` message of round `v.round`.
It assumed here that the proposer of `v` broadcasts a `PROPOSAL` message at
time `v.time`, according to its local clock, so that every correct process
should receive this message by time `v.time + MSGDELAY + PRECISION`, according
to their local clocks.
Back to [main document][main].