Linearizability Linearizability The result of each execution is equivalent to a

# Linearizability linearizability the result of each

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Linearizability Linearizability. The result of each execution is equivalent to a sequential execution that respects the real-time precedence (i.e., in which an operation returning before another is invoked is always ordered before) is the same as if the (read and write) operations by all processes on the same data store were executed in some sequential order and the operations of each individual process appear in this sequence in its program order Example 6 : this is a linearizable execution (initially x=0) 4 Linearizability (of reads and writes) p 0 time p 1 R(x)0 R(x) 1 W(x)1 The University of Sydney Page 46 Linearizability. The result of each execution is equivalent to a sequential execution that respects the real-time precedence (i.e., in which an operation returning before another is invoked is always ordered before) is the same as if the (read and write) operations by all processes on the same data store were executed in some sequential order and the operations of each individual process appear in this sequence in its program order Example 7 : is this a linearizable execution? (initially x=0) Linearizability 4 Linearizability (of reads and writes) p 0 time p 1 R(x)1 R(x)1 W(x)1 The University of Sydney Page 47 Linearizability Linearizability. The result of each execution is equivalent to a sequential execution that respects the real-time precedence (i.e., in which an operation returning before another is invoked is always ordered before) is the same as if the (read and write) operations by all processes on the same data store were executed in some sequential order and the operations of each individual process appear in this sequence in its program order Example 7 : this is a linearizable execution (initially x=0) R 0 (x)1 is concurrent with W 1 (x)1 (none precedes the other w.r.t real-time), hence R 0 (x) can return 1 (or 0) without violating linearizability 4 Linearizability (of reads and writes) p 0 time p 1 R(x)1 R(x)1 W(x)1 The University of Sydney Page 48 Linearizability can also apply to other kind of operations. Consider an integer set object that exports (as opposed to the previous register exporting read/write): insert(int a)boolean b that adds an element to the set if not already present and return true, returns false if already present delete(int a)boolean b that removes an integer from the set if it is currently present and returns true, false if not present contains(int a)boolean b that checks whether an integer is present in the set Example 8 : is this a linearizable execution of set operations? (initially x set) Linearizability 4 Linearizability (of higher level operations) p 0 time p 1 insert(x)true contains(x)true remove(x)true
6/5/18 13 The University of Sydney Page 49 Linearizability can also apply to other kind of operations.

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