Proving linearisability via coarse-grained abstraction

Linearisability has become the standard safety criterion for concurrent data structures ensuring that the effect of a concrete operation takes place after the execution some atomic statement (often referred to as the linearisation point). Identification of linearisation points is a non-trivial task and it is even possible for an operation to be linearised by the execution of other concurrent operations. This paper presents a method for verifying linearisability that does not require identification of linearisation points in the concrete code. Instead, we show that the concrete program is a refinement of some coarse-grained abstraction. The linearisation points in the abstraction are straightforward to identify and the linearisability proof itself is simpler due to the coarse granularity of its atomic statements. The concrete fine-grained program is a refinement of the coarse-grained program, and hence is also linearisable because every behaviour of the concrete program is a possible behaviour its abstraction.