We examine verification of concurrent programs under the total store ordering (TSO) semantics used by the x86 architecture. In our model, threads manipulate variables over infinite domains and they can check whether variables are related for a range of relations. We show that, in general, the control state reachability problem is undecidable. This result is derived through a reduction from the state reachability problem of lossy channel systems with data (which is known to be undecidable). In the light of this undecidability, we turn our attention to a more tractable variant of the reachability problem. Specifically, we study context bounded runs, which provide an under-approximation of the program behavior by limiting the possible interactions between processes. A run consists of a number of contexts, with each context representing a sequence of steps where a only single designated thread is active. We prove that the control state reachability problem under bounded context switching is PSPACE complete.

中文翻译：

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具有无限数据域的 TSO 验证

我们检查 x86 架构使用的全存储排序 (TSO) 语义下并发程序的验证。在我们的模型中，线程在无限域上操作变量，并且它们可以检查变量是否与一系列关系相关。我们表明，一般来说，控制状态可达性问题是不可判定的。该结果是通过减少有数据的有损信道系统的状态可达性问题（已知这是不可判定的）而得出的。鉴于这种不确定性，我们将注意力转向可达性问题的更容易处理的变体。具体来说，我们研究上下文有界运行，它通过限制进程之间可能的交互来提供程序行为的欠近似。一次运行由多个上下文组成，每个上下文代表一系列步骤，其中只有一个指定的线程处于活动状态。我们证明了有界上下文切换下的控制状态可达性问题是PSPACE完备的。