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The CAP theorem is based on three trade-offs, one of which is "atomic consistency" (shortened to "consistency" for the acronym), about which the authors note, "Discussing atomic consistency is somewhat different than talking about an ACID database, as database consistency refers to transactions, while atomic consistency refers only to a property of a single request/response operation sequence.
Note that consistency as defined in the CAP theorem is quite different from the consistency guaranteed in ACID database transactions. [4] Availability Every request received by a non-failing node in the system must result in a response. This is the definition of availability in CAP theorem as defined by Gilbert and Lynch. [1]
C-theorem ; CAP theorem (theoretical computer science) CPCTC (triangle geometry) Cameron–Erdős theorem (discrete mathematics) Cameron–Martin theorem (measure theory) Cantor–Bernstein–Schroeder theorem (set theory, cardinal numbers) Cantor's intersection theorem (real analysis) Cantor's isomorphism theorem (order theory)
The tradeoff between availability, consistency and latency, as described by the PACELC theorem. In database theory, the PACELC theorem is an extension to the CAP theorem.It states that in case of network partitioning (P) in a distributed computer system, one has to choose between availability (A) and consistency (C) (as per the CAP theorem), but else (E), even when the system is running ...
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
State-based CRDTs (also called convergent replicated data types, or CvRDTs) are defined by two types, a type for local states and a type for actions on the state, together with three functions: A function to produce an initial state, a merge function of states, and a function to apply an action to update a state.
In 2002, Seth Gilbert and Nancy Lynch of MIT published a formal proof of Brewer's conjecture, rendering it a theorem. This last claim has been criticized, however, this reference does not offer a peer-reviewed formal proof – just an informal assertion on a blog posting.
Pages in category "Theorems in real analysis" The following 45 pages are in this category, out of 45 total. ... Fatou–Lebesgue theorem; Fermat's theorem (stationary ...