一小段关于linearizability的解释

https://pdos.csail.mit.edu/6.824/notes/l-raft2.txt

https://www.anishathalye.com/2017/06/04/testing-distributed-systems-for-linearizability/

https://pdos.csail.mit.edu/6.824/papers/zookeeper-faq.txt

满足linearizability的要求是:

  1. 可以对executions进行定序
  2. 这个序列满足: a)时间要求 b)写入之后才可见的要求
we need a definition of "correct" for Lab 3 &c
  how should clients expect Put and Get to behave?
  often called a consistency contract
  helps us reason about how to handle complex situations correctly
    e.g. concurrency, replicas, failures, RPC retransmission,
         leader changes, optimizations
  we'll see many consistency definitions in 6.824

"linearizability" is the most common and intuitive definition
  formalizes behavior expected of a single server ("strong" consistency)

linearizability definition:
  an execution history is linearizable if
    one can find a total order of all operations,
    that matches real-time (for non-overlapping ops), and
    in which each read sees the value from the
    write preceding it in the order.

a history is a record of client operations, each with
  arguments, return value, time of start, time completed

example history 1:
  |-Wx1-| |-Wx2-|
    |---Rx2---|
      |-Rx1-|
"Wx1" means "write value 1 to record x"
"Rx1" means "a read of record x yielded value 1"
draw the constraint arrows:
  the order obeys value constraints (W -> R)
  the order obeys real-time constraints (Wx1 -> Wx2)
this order satisfies the constraints:
  Wx1 Rx1 Wx2 Rx2
  so the history is linearizable

note: the definition is based on external behavior
  so we can apply it without having to know how service works
note: histories explicitly incorporates concurrency in the form of
  overlapping operations (ops don't occur at a point in time), thus good
  match for how distributed systems operate.

example history 2:
  |-Wx1-| |-Wx2-|
    |--Rx2--|
              |-Rx1-|
draw the constraint arrows:
  Wx1 before Wx2 (time)
  Wx2 before Rx2 (value)
  Rx2 before Rx1 (time)
  Rx1 before Wx2 (value)
there's a cycle -- so it cannot be turned into a linear order. so this
history is not linearizable. (it would be linearizable w/o Rx2, even
though Rx1 overlaps with Wx2.)

example history 3:
|--Wx0--|  |--Wx1--|
            |--Wx2--|
        |-Rx2-| |-Rx1-|
order: Wx0 Wx2 Rx2 Wx1 Rx1
so the history linearizable.
so:
  the service can pick either order for concurrent writes.
  e.g. Raft placing concurrent ops in the log.

example history 4:
|--Wx0--|  |--Wx1--|
            |--Wx2--|
C1:     |-Rx2-| |-Rx1-|
C2:     |-Rx1-| |-Rx2-|
what are the constraints?
  Wx2 then C1:Rx2 (value)
  C1:Rx2 then Wx1 (value)
  Wx1 then C2:Rx1 (value)
  C2:Rx1 then Wx2 (value)
  a cycle! so not linearizable.
so:
  service can choose either order for concurrent writes
  but all clients must see the writes in the same order
  this is important when we have replicas or caches
    they have to all agree on the order in which operations occur

example history 5:
|-Wx1-|
        |-Wx2-|
                |-Rx1-|
constraints:
  Wx2 before Rx1 (time)
  Rx1 before Wx2 (value)
  (or: time constraints mean only possible order is Wx1 Wx2 Rx1)
there's a cycle; not linearizable
so:
  reads must return fresh data: stale values aren't linearizable
  even if the reader doesn't know about the write
    the time rule requires reads to yield the latest data
  linearzability forbids many situations:
    split brain (two active leaders)
    forgetting committed writes after a reboot
    reading from lagging replicas

example history 6:
suppose clients re-send requests if they don't get a reply
in case it was the response that was lost:
  leader remembers client requests it has already seen
  if sees duplicate, replies with saved response from first execution
but this may yield a saved value from long ago -- a stale value!
what does linearizabilty say?
C1: |-Wx3-|          |-Wx4-|
C2:          |-Rx3-------------|
order: Wx3 Rx3 Wx4
so: returning the old saved value 3 is correct

You may find this page useful:
https://www.anishathalye.com/2017/06/04/testing-distributed-systems-for-linearizability/

两个概念linearizability和serializability之间的区别是什么(说实话我也是一知半解)

Q: How does linearizability differ from serializability?

A: The usual definition of serializability is much like
linearizability, but without the requirement that operations respect
real-time ordering. Have a look at this explanation:
http://www.bailis.org/blog/linearizability-versus-serializability/