The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous programs that capture all known results as well as show decidability of new and important classes. As a main consequence, we show decidability of safety, termination and boundedness verification for higher-order asynchronous programs -- such as OCaml programs using Lwt -- and undecidability of liveness verification already for order-2 asynchronous programs. We show that under mild assumptions, surprisingly, safety and termination verification of asynchronous programs with handlers from a language class are decidable iff emptiness is decidable for the underlying language class. Moreover, we show that configuration reachability and liveness (fair termination) verification are equivalent, and decidability of these problems implies decidability of the well-known "equal-letters" problem on languages. Our results close the decidability frontier for asynchronous programs.

中文翻译：

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异步共享内存程序的一般可判定性结果：高阶和更高阶

从底层系统软件到高层Web编程，异步编程模型出现在许多情况下。我们从语言理论的角度出发，显示异步程序的一般可判定性和不可判定性结果，这些异步程序捕获所有已知结果，并显示新的和重要类的可判定性。作为一个主要的结果，我们显示了对高阶异步程序（例如使用Lwt的OCaml程序）的安全性，终止和有界性验证的可判定性，以及对于2阶异步程序的活动性验证的不确定性。我们表明，在温和的假设下，令人惊讶的是，使用语言类的处理程序对异步程序的安全性和终止验证是可以确定的，而对于基础语言类则可以确定为空。此外，我们表明配置可达性和活动性（公平终止）验证是等效的，并且这些问题的可判定性意味着语言上众所周知的“等式”问题的可判定性。我们的结果关闭了异步程序的可判定性边界。