Modular Verification of Concurrency-Aware Linearizability

Linearizability is the de facto correctness condition for concurrent objects. Informally, linearizable objects provide the illusion that each operation takes effect instantaneously at a unique point in time between its invocation and response. Hence, by design, linearizability cannot describe behaviors of concurrency-aware concurrent objects CA-objects, objects in which several overlapping operations "seem to take effect simultaneously". In this paper, we introduce concurrency-aware linearizability CAL, a generalized notion of linearizability which allows to formally describe the behavior of CA-objects. Based on CAL, we develop a thread- and procedure-modular verification technique for reasoning about CA-objects and their clients. Using our new technique, we present the first proof of linearizability of the elimination stack of Hendler et al.i¾?[10] in which the stack's elimination subcomponent, which is a general-purpose CA-object, is specified and verified independently of its particular usage by the stack.

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