Order out of Chaos: Proving Linearizability Using Local Views
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Proving the linearizability of highly concurrent data structures, such as those using optimistic concurrency control, is a challenging task. The main difficulty is in reasoning about the view of the memory obtained by the threads, because as they execute, threads observe different fragments of the data structure from different points in time. Until today, every linearizability proof has tackled this challenge from scratch. We present a unifying proof argument capable of proving the linearizability of several highly concurrent data structures, including an optimistic self-balancing binary search tree and the Lazy List algorithm. Our framework facilitates sequential reasoning about the view of a thread, as if it traverses the data structure without interference from other operations. Our key contribution is showing that properties of reachability along search paths can be deduced for concurrent traversals from interference-free traversals. This greatly simplifies linearizability proofs. At the heart of our proof method lies a notion of order on the memory, corresponding to the order in which locations in memory are read by the threads, which guarantees a certain notion of consistency between the view of the thread and the actual memory. To apply our framework, the user proves that the data structure satisfies certain conditions, relating to acyclicity of the data structure and the preservation of search paths to locations affected by interfering writes. Establishing the conditions, as well as the full linearizability proof, reduces to simple concurrent reasoning. The result is a clear and comprehensible correctness proof. Our framework elucidates common patterns underlying several existing data structures, and could pave the way to design new data structures based on these principles.
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