Distributed Systems Fall 2022
Lecture 4: Linearizability and CAP Theorem

# Herlihy and Wing: Linearizability: A Correctness Condition for Concurrent Objects

It is important that you read and understand this paper carefully since
linearizability is going to show up frequently as a correctness condition for
the protocols we study in class, and most systems designed, built and deployed
today have to choose whether or not to trade-off linearizability for performance
and fault-tolerance.

Linearizability is a correctness property expressed in terms of operations on
abstract data types (objects) that provide some atomic operations. The paper
uses FIFO queues as a running example, which provide enqueue and dequeue as
atomic operations. The paper assumes an environment where several concurrent
processes can enqueue and dequeue elements, this might be a distributed system
or even just a multi-threaded application, and asks what does it mean for the
queue to be **correct**. The paper's criterion is linearizability, which means
that (a) there is a linear order in which the operations seem to have occurred;
and (b) this linear order is consistent with real-time, i.e., an operation
occurs before the queue returns to the caller. These two seemingly simple
conditions have several implications about how locality, but also has
implications about the fault tolerance and performance of objects providing this
guarantee.

## Questions:
For the following questions consider a stack (a last-in-first-out data
structure) and provide an example of:

(a) A linearizable operation history for the stack.
(b) An operation history that is not linearizable.
(c) Pseudo-code for a (single-machine) implementation of such a stack.

# Gilbert and Lynch: Brewer’s Conjecture and the Feasibility of Consistent, Available, Partition-Tolerant Web Services

The CAP theorem was informally stated by Eric Brewer in PODC 2000, and reflected
his experiences building Inktomi (an early search engine) as a distributed
service running on multiple machines. Owing to the informal manner in which it
was stated this theorem continues to be fodder for internet debates to this
date. The Gilbert and Lynch paper formalizes this notion and talks about how
linearizability and availability are at odds, and how the situation is better in
a partially synchronous network. The CAP theorem is often cited as a reason why
so called NoSQL databases moved away from linearizability, and this paper
demonstrates how Herlihy and Wing's correctness criterion can impact system
design.

## Questions:
(d) State the CAP theorem, as formalized, by Gilbert and Lynch?