A generic register automaton is a finite automaton equipped with variables (which may be viewed as counters or, more generally, registers) ranging over infinite data domains. A trace of a generic register automaton is an alternating sequence of alphabet symbols and values taken by the variables during an execution of the automaton. The problem addressed in this paper is the inclusion between the sets of traces (data languages) recognized by such automata. Since the problem is undecidable in general, we give a semi-algorithm based on a combination of abstraction refinement and antichains, which is proved to be sound and complete, but whose termination is not guaranteed. Moreover, we further enhance the proposed algorithm by exploiting a concept of data simulations, i.e., simulation relations aware of the data associated with the words. We have implemented our technique in a prototype tool and show promising results on multiple non-trivial examples.

中文翻译：

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用于跟踪包含无限状态系统的抽象细化和反链

通用寄存器自动机是一种有限自动机，它配备了跨越无限数据域的变量（可以被视为计数器或更一般地，寄存器）。通用寄存器自动机的踪迹是在自动机执行期间由变量取的字母符号和值的交替序列。本文解决的问题是包含在此类自动机识别的轨迹集（数据语言）之间。由于问题一般是不可判定的，我们给出了一个基于抽象细化和反链相结合的半算法，该算法被证明是健全的和完备的，但其终止并没有得到保证。此外，我们通过利用数据模拟的概念，即知道与词相关的数据的模拟关系，进一步增强了所提出的算法。