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=== Order of actions ===
Time-order between two operations can be represented by an ''[[ordered pair]]'' of these operations (e.g., the existence of a pair (OP1, OP2) means that OP1 is always before OP2), and a schedule in the general case is a [[set (mathematics)|set]] of such ordered pairs. Such a set, a schedule, is a [[partial order]] which can be represented by an ''[[acyclic directed graph]]'' (or ''directed acyclic graph'', DAG) with operations as nodes and time-order as a [[directed edge]] (no cycles are allowed since a cycle means that a first (any) operation on a cycle can be both before and after (any) another second operation on the cycle, which contradicts our perception of [[Time]]). In many cases, a graphical representation of such a graph is used to demonstrate a schedule.
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Serializability is used to keep the data in the data item in a consistent state
If any specific order between some transactions is requested by an application, then it is enforced independently of the underlying serializability mechanisms. These mechanisms are typically indifferent to any specific order, and generate some unpredictable [[partial order]] that is typically compatible with multiple serial orders of these transactions. This partial order results from the scheduling orders of concurrent transactions' data access operations, which depend on many factors.
Serializability is used in
'''Serializability theory''' provides the formal framework to reason about and analyze serializability and its techniques
====Conflicting actions====
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==== Distributed serializability ====
'''Distributed serializability''' is the serializability of a schedule of a transactional [[Distributed computing|distributed system]] (e.g., a [[distributed database]] system). Such a system is characterized by ''[[distributed transaction]]s'' (also called ''global transactions''), i.e., transactions that span computer processes (a process abstraction in a general sense, depending on computing environment; e.g., [[operating system]]'s [[Thread (computer science)|thread]]) and possibly network nodes. A distributed transaction comprises more than one of several ''local sub-transactions'' that each has states as described above for a [[
Distributed serializability is achieved by implementing distributed versions of the known centralized techniques.<ref name="Bernstein872"/><ref name="Weikum012"/> Typically, all such distributed versions require utilizing conflict information (of either materialized or non-materialized conflicts, or, equivalently, transaction precedence or blocking information; conflict serializability is usually utilized) that is not generated locally, but rather in different processes, and remote locations. Thus information distribution is needed (e.g., precedence relations, lock information, timestamps, or tickets). When the distributed system is of a relatively small scale and message delays across the system are small, the centralized concurrency control methods can be used unchanged while certain processes or nodes in the system manage the related algorithms. However, in a large-scale system (e.g., ''grid'' and ''cloud''), due to the distribution of such information, a substantial performance penalty is typically incurred, even when distributed versions of the methods (vs. the centralized ones) are used, primarily due to computer and communication [[Latency (engineering)|latency]]. Also, when such information is distributed, related techniques typically do not scale well. A well-known example with respect to scalability problems is a [[distributed lock manager]], which distributes lock (non-materialized conflict) information across the distributed system to implement locking techniques.
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