Atomic semantics is a type of guarantee provided by a data register shared by several processors in a parallel machine or in a network of computers working together. Atomic semantics are very strong. An atomic register provides strong guarantees even when there is concurrency and failures. A read/write register R stores a value and is accessed by two basic operations: read and write(v). A read returns the value stored in R and write(v) changes the value stored in R to v. A register is called atomic if it satisfies the two following properties: 1) Each invocation op of a read or write operation: •Must appear as if it were executed at a single point τ(op) in time. •τ (op) works as follow: τb(op) ≤ τ (op) ≤ τe(op): where τb(op) and τe(op) indicate the time when the operation op begins and ends. •If op1 ≠ op2, then τ (op1)≠τ (op2) 2) Each read operation returns the value written by the last write operation before the read, in the sequence where all operations are ordered by their τ values. Atomic/Linearizable register: Termination: when a node is correct,sooner or later each read and write operation will complete. Safety Property (Linearization points for read and write and failed operations): Read operation:It appears as if happened at all nodes at some times between the invocation and response time. Write operation: Similar to read operation,it appears as if happened at all nodes at some times between the invocation and response time. Failed operation(The atomic term comes from this notion):It appears as if it is completed at every single node or it never happened at any node. Example : We know that an atomic register is one that is linearizable to a sequential safe register. The following picture shows where we should put the linearization point for each operation: An atomic register could be defined for a variable with a single writer but multi- readers(SWMR),single-writer/single-reader (SWSR),or multi-writer/multi-reader(MWMR). Here is an example of a multi-reader multi-writer atomic register which is accessed by three processes (P1,P2,P3).Note that R.read() → v means that the corresponding read operation returns v, which is the value of the register. Therefore, the following execution of the register R could satisfies the definition of the atomic registers: R.write(1), R.read()→1, R.write(3), R.write(2), R.read()→2, R.read()→2.
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