We present a thread-modular proof method for complexity and resource bound analysis of concurrent, shared-memory programs. To this end, we lift Jones’ rely-guarantee reasoning to assumptions and commitments capable of expressing bounds. The compositionality (thread-modularity) of this framework allows us to reason about parameterized programs, i.e., programs that execute arbitrarily many concurrent threads. We automate reasoning in our logic by reducing bound analysis of concurrent programs to the sequential case. As an application, we automatically infer time complexity for a family of fine-grained concurrent algorithms, lock-free data structures, to our knowledge for the first time.

我们提出了一种用于并行和共享内存程序的复杂性和资源绑定分析的线程模块化证明方法。为此，我们将琼斯的依赖保证推理提升为能够表达界限的假设和承诺。该框架的组合性（线程模块化）使我们能够推理参数化程序，即，任意执行许多并发线程的程序。通过将并发程序的绑定分析减少到顺序情况，我们使逻辑自动推理。作为应用程序，我们首次自动推断出一系列细粒度的并发算法，无锁数据结构的时间复杂度。