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	~~'''~~Linearizability''' is a concept in [[computer science]] and [[distributed systems]] that pertains to the behavior of systems where operations appear to occur instantaneously at some point between their invocation and their response. It is a correctness condition for concurrent objects that extends the notion of atomicity from [[transaction processing]] systems to objects in concurrent systems. Linearizability is a strong form of [[consistency (computer science)\|consistency]] and [[serializability]], ensuring that once an operation has completed, all subsequent operations will see the effect of that operation. This concept is crucial for understanding the behavior of concurrent systems and for designing systems that behave correctly in the presence of concurrency.		{{DISPLAYTITLE:Linearizability}}

	==~~Definition~~==		== Linearizability ==
	Linearizability, also known as atomic consistency or strong consistency, requires that completed operations (or transactions) appear to be instantaneous, happening at some single, indivisible point in time between their start and finish. This implies that if an operation ''B'' starts after another operation ''A'' has finished, then ''B'' must see the system in a state that reflects the changes made by ''A''. In other words, operations are linearizable if their effects occur in a total order that is consistent with the order of their invocations.

	~~==Properties==~~		[[File:Linearlizable_Process.svg\|thumb\|right\|Illustration of a linearizable process]]
	~~Linearizability has several key properties that make it desirable for concurrent systems~~:
	* '''Non-blocking:''' Linearizable systems often implement non-blocking or lock-free algorithms, allowing the system to continue operating even when parts of ~~it are failing or are slow.~~
	* '''Composability:''' Linearizable operations can be composed into larger linearizable ~~operations, making it easier to reason about complex systems.~~
	* '''Local reasoning:''' Because operations appear atomic, reasoning about system state can be done locally, without considering the global state of the system.

	~~==Applications==~~		'''Linearizability''' is a [[consistency model]] for [[concurrent computing]] systems. It is a correctness condition for [[concurrent data structures]] that ensures that operations appear to occur instantaneously at some point between their invocation and their response. This property is crucial for reasoning about the behavior of concurrent systems and ensuring that they behave in a predictable manner.
	Linearizability is ~~applied in various areas of computing, including:~~
	* [[~~Distributed databases~~]] ~~and~~ [[~~transaction processing~~]] systems~~, where it ensures that transactions are processed reliably and in a manner consistent with~~ a ~~single, centralized database.~~
	* [[~~Concurrent~~ data structures]]~~, such as lock-free queues and stacks, where it guarantees~~ that operations by concurrent ~~threads are correctly ordered.~~
	* [[Distributed consensus algorithms]], like [[Paxos (computer science)\|Paxos]] and ~~[[Raft (computer science)\|Raft]], which rely on linearizability to ensure~~ that ~~all nodes~~ in a ~~distributed system agree on a single source of truth~~.

	==~~Challenges~~==		== Definition ==
	~~Implementing linearizability~~ in distributed systems ~~comes with challenges:~~
	* '''Performance:''' Ensuring linearizability can introduce latency, as operations may need to ~~wait for confirmation from other parts of the system~~ to ensure ~~their actions are correctly ordered~~.		Linearizability is defined in terms of [[atomic operations]] on shared [[data structures]]. An operation is said to be linearizable if it can be ordered in a sequence that respects the real-time ordering of operations and each operation appears to take effect instantaneously at some point between its invocation and its completion.
	* '''Fault tolerance:''' Designing linearizable systems that ~~can handle failures~~, such as ~~network partitions or node crashes~~, ~~requires sophisticated algorithms~~ and ~~often results~~ in ~~trade-offs with performance~~.
			In a linearizable system, each operation on a [[shared object]] appears to take effect at a single, indivisible point in time, even though the operation may actually take some time to execute. This point is called the "linearization point."

			== Importance in Concurrent Systems ==

			Linearizability is important in concurrent systems because it provides a simple and intuitive way to reason about the behavior of concurrent operations. It allows developers to think about operations as if they were executed in a sequential order, even though they are actually executed concurrently.

			This property is particularly useful in [[distributed systems]], where operations may be executed on different nodes and need to be coordinated to ensure consistency. Linearizability provides a strong guarantee that helps in building reliable and predictable distributed applications.

			== Linearizability vs. Sequential Consistency ==

			Linearizability is often compared to [[sequential consistency]], another consistency model for concurrent systems. While both models ensure that operations appear to occur in a specific order, linearizability is a stronger condition because it respects the real-time ordering of operations.

			Sequential consistency only requires that the result of any execution is the same as if the operations of all the processes were executed in some sequential order, but it does not require that this order respects the real-time order of operations. Linearizability, on the other hand, requires that the order of operations respects the real-time order, making it a stricter and more intuitive model.

			== Applications ==

			Linearizability is used in the design of [[concurrent data structures]] such as [[queues]], [[stacks]], and [[hash tables]]. It is also used in the implementation of [[distributed databases]] and [[transactional memory systems]].

			By ensuring that operations on these data structures are linearizable, developers can guarantee that the system behaves in a predictable and reliable manner, even in the presence of concurrent operations.

			== Related pages ==

	~~==See Also==~~
	* [[Consistency model]]		* [[Consistency model]]
	* [[~~Serializability~~]]		* [[Concurrent computing]]
	* [[~~CAP theorem~~]]		* [[Distributed system]]
	* [[~~Distributed computing~~]]		* [[Sequential consistency]]
			* [[Atomic operation]]
	~~==References==~~
	~~<references/>~~

	[[Category:~~Computer science~~]]		[[Category:Concurrency control]]
	[[Category:Distributed computing]]		[[Category:Distributed computing]]
	~~{{computer-science-stub}}~~

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'''Linearizability''' is a concept in [[computer science]] and [[distributed systems]] that pertains to the behavior of systems where operations appear to occur instantaneously at some point between their invocation and their response. It is a correctness condition for concurrent objects that extends the notion of atomicity from [[transaction processing]] systems to objects in concurrent systems. Linearizability is a strong form of [[consistency (computer science)|consistency]] and [[serializability]], ensuring that once an operation has completed, all subsequent operations will see the effect of that operation. This concept is crucial for understanding the behavior of concurrent systems and for designing systems that behave correctly in the presence of concurrency.

==Definition==
Linearizability, also known as atomic consistency or strong consistency, requires that completed operations (or transactions) appear to be instantaneous, happening at some single, indivisible point in time between their start and finish. This implies that if an operation ''B'' starts after another operation ''A'' has finished, then ''B'' must see the system in a state that reflects the changes made by ''A''. In other words, operations are linearizable if their effects occur in a total order that is consistent with the order of their invocations.

==Properties==
Linearizability has several key properties that make it desirable for concurrent systems:
* '''Non-blocking:''' Linearizable systems often implement non-blocking or lock-free algorithms, allowing the system to continue operating even when parts of it are failing or are slow.
* '''Composability:''' Linearizable operations can be composed into larger linearizable operations, making it easier to reason about complex systems.
* '''Local reasoning:''' Because operations appear atomic, reasoning about system state can be done locally, without considering the global state of the system.

==Applications==
Linearizability is applied in various areas of computing, including:
* [[Distributed databases]] and [[transaction processing]] systems, where it ensures that transactions are processed reliably and in a manner consistent with a single, centralized database.
* [[Concurrent data structures]], such as lock-free queues and stacks, where it guarantees that operations by concurrent threads are correctly ordered.
* [[Distributed consensus algorithms]], like [[Paxos (computer science)|Paxos]] and [[Raft (computer science)|Raft]], which rely on linearizability to ensure that all nodes in a distributed system agree on a single source of truth.

==Challenges==
Implementing linearizability in distributed systems comes with challenges:
* '''Performance:''' Ensuring linearizability can introduce latency, as operations may need to wait for confirmation from other parts of the system to ensure their actions are correctly ordered.
* '''Fault tolerance:''' Designing linearizable systems that can handle failures, such as network partitions or node crashes, requires sophisticated algorithms and often results in trade-offs with performance.

==See Also==
* [[Consistency model]]
* [[Serializability]]
* [[CAP theorem]]
* [[Distributed computing]]

==References==
<references/>

[[Category:Computer science]]
[[Category:Distributed computing]]
{{computer-science-stub}}

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