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The instant used to identify an operation's abstract effect in a proof of linearizability. Loading the published pointer can be the linearization point of an immutable snapshot read, with suitable ordering and lifetime guarantees.

O1 supplies mutual exclusion over each complete operation. A reader sees the protected state from a serial order of readers and writers; a writer can safely mutate the existing object while holding the common mutex. If an update reads the old state and modifies it, the entire read-modify-write can be protected against a lost update.

O2 has different semantics. Assume an indivisible aligned access to p, correct publication ordering, and no later mutation of a published version. A reader chooses one version when it loads p; the subsequent load instructions use the same saved pointer, so an overlapping writer need not block that reader. The reader may continue observing the old complete version after the writer has published the new one. A sufficiently specified snapshot read can still be linearizable, with the load of p as its linearization point: a read overlapping a write is allowed to come before that write in the abstract order. Thus reading an old version during overlap does not by itself prove failure of linearizability.

Multiple writers can each construct a valid replacement and race to publish it. If the operation is simply “replace the whole object”, atomic pointer stores give a last-publication order. If each writer instead computes a change from the previously published state, O2 alone does not preserve both changes. Two writers can both read a counter value zero, independently build a version containing one, and publish their respective versions; the final counter is one. A writer mutex or compare-and-swap with retry is needed when the required operation must avoid that lost update. Memory barriers alone do not provide this exclusion.

Releasing the old object's computer memory immediately after publishing a replacement is unsafe. For example:The final operation is a use-after-free: it may crash, see allocator metadata, or read a different object that reuses the same memory address. An atomic update of p does not update the reader's already copied pointer. Freeing the new object immediately would of course also invalidate p itself.

Publication and reclamation are separate: publish a fully initialized version, and retain every old version until all readers that might hold it have finished. A read-copy-update grace period or a suitable hazard pointer protocol can provide that lifetime guarantee; naive reference-count acquisition after loading an unprotected pointer can itself race with freeing. Correct memory barriers in part (iii) ensure visibility, not object lifetime.

Use one monitor to protect both the occupied flag and the slot. Option supplies an empty marker without confusing an empty slot with a valid null payload.

class MonitorMemory[T] extends Memory[T] {
  private var slot: Option[T] = None
  def write(msg: T): Unit = synchronized {
    while (slot.nonEmpty) wait()
    slot = Some(msg)
    notifyAll()
  }
  def read: T = synchronized {
    while (slot.isEmpty) wait()
    val result = slot.get
    slot = None
    notifyAll()
    result
  }
}

A writer changes empty to full while holding the monitor; a reader changes full to empty while holding the same monitor. The corresponding successful assignment or removal is its linearization point. No second writer can overwrite a full slot, and no two readers can remove one value. Rechecking in a while handles spurious wakeups and competition after notification.

There are two different waiting predicates on the same monitor: writers need empty, readers need full. A single arbitrary notify could wake a caller of the wrong kind. For example, after a reader empties the slot, waking another reader leaves it waiting again while a writer remains asleep, potentially stranding the computation. notifyAll prevents that lost wake-up pattern by allowing every waiter to recheck. Thus,With many users, each change wakes numerous software threads even though at most one can use that new slot state. Most reacquire the monitor, find their predicate false and sleep again. This thundering herd wastes context switches and lock acquisitions. It also supplies no fairness or arrival-order guarantee.