On Sequentializing Concurrent Programs

Abstract

We propose a general framework for compositional underapproximate concurrent program analyses by reduction to sequential program analyses—so-called sequentializations. We notice the existing sequentializations—based on bounding the number of execution contexts, execution rounds, or delays from a deterministic task-schedule—rely on three key features for scalable concurrent program analyses: (i) reduction to the sequential program model, (ii) compositional reasoning to avoid expensive task-product constructions, and (iii) parameterized exploration bounds. To understand how those sequentializations can be unified and generalized, we define a general framework which preserves their key features, and in which those sequentializations are particular instances. We also identify a most general instance which considers more executions, by composing the rounds of different tasks in any order, restricted only by the unavoidable program and task-creation causality orders. In fact, we show this general instance is fundamentally more powerful by identifying an infinite family of state-reachability problems (to states g ₁, g ₂,...) which can be answered precisely with a fixed exploration bound, whereas the existing sequentializations require an increasing bound k to reach each g _k . Our framework applies to a general class of shared-memory concurrent programs, with dynamic task-creation and arbitrary preemption.