Lecture 08: Concurrent Objects 3

Outline

  1. Sequential Consistency
  2. Linearizability
  3. Progress Conditions

Last Time

What is “correct” behavior for a concurrent execution of a data structure?

Sequential Consistency

Two Natual Desiderata

Method calls/responses consistent with some sequential execution

Method calls can be ordered such that:

  1. they are consistent with program order

    • if a single thread calls methodOne() before methodTwo(), then methodOne() $\to$ methodTwo() in sequential execution

  2. pre/post conditions for each method call satisfy data structure’s sequential specification

Such executions are sequentially consistent

Definition

An execution is sequentially consistent if all method calls can be ordered such that:

  1. they are consistent with program order
  2. they meet object’s sequential specification

An implementation of an object is sequentially consistent if it guarantees every execution is sequentially consistent

Example

What are possible outcomes of deq() calls in a sequentially consistent execution?

Sequential Consistency is Weak

  • Method calls can appear interleaved in any order that maintains program order
  • No guarantees for “real time” order
    • (partially) order methods w.r.t. real time

Sequential Consistency is Nonblocking

Consider concurrent execution:

  • Pending method call (invoked, but no response yet)
  • Then: exists a response that can be made immediately that does not violate SC

It is possible to achieve SC without needing to wait for response from other pending methods

  • May still be difficult to figure out which response will give SC execution

Nonblocking Example

A Subtler Issue

Suppose we have a program two queues, p and q

  • Implementation of queue guarantees sequentially consistency

Must an execution of a program with p and q be sequentially consistent?

An Execution

Sequentially Consistent for p

Sequentially Consistent for q

But is Execution SC?

Sequential Consistency is not Compositional

A property $\mathcal{P}$ is compositional if

  • Whenever all objects in system satisfy $\mathcal{P}$, then system satisfies $\mathcal{P}$

Previous example shows:

  • Sequential consistency is not compositional

Sequential Consistency Is…

  • …Maybe the weakest reasonble guarantee we could expect of a concurrent implementation of an object
  • …Potentially allows for a lot of parallelism
    • SC is a nonblocking property
  • …Not compositional
    • a system made of SC components need not be SC!