In recent times, satisfiability modulo theories (SMT) techniques gained increasing attention and obtained remarkable success in model-checking infinite-state systems. Still, we believe that whenever more expressivity is needed in order to specify the systems to be verified, more and more support is needed from mathematical logic and model theory. This is the case of the applications considered in this paper: we study verification over a general model of relational, data-aware processes, to assess (parameterized) safety properties irrespectively of the initial database (DB) instance. Toward this goal, we take inspiration from array-based systems and tackle safety algorithmically via backward reachability. To enable the adoption of this technique in our rich setting, we make use of the model-theoretic machinery of model completion, which surprisingly turns out to be an effective tool for verification of relational systems and represents the main original contribution of this paper. In this way, we pursue a twofold purpose. On the one hand, we isolate three notable classes for which backward reachability terminates, in turn witnessing decidability. Two of such classes relate our approach to conditions singled out in the literature, whereas the third one is genuinely novel. On the other hand, we are able to exploit SMT technology in implementations, building on the well-known MCMT (Model Checker Modulo Theories) model checker for array-based systems and extending it to make all our foundational results fully operational. All in all, the present contribution is deeply rooted in the long-standing tradition of the application of model theory in computer science. In particular, this paper applies these ideas in an original mathematical context and shows how these techniques can be used for the first time to empower algorithmic techniques for the verification of infinite-state systems based on arrays, so as to make such techniques applicable to the timely, challenging settings of data-aware processes.

中文翻译：

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基于 SMT 的数据感知流程验证：模型理论方法

最近，可满足性模理论 (SMT) 技术越来越受到关注，并在模型检查无限状态系统方面取得了显著成功。尽管如此，我们认为，每当需要更多的表达能力来指定要验证的系统时，就需要越来越多的数学逻辑和模型理论的支持。这是本文考虑的应用程序的情况：我们研究了对关系、数据感知过程的一般模型的验证，以评估（参数化）安全属性，而与初始数据库 (DB) 实例无关。为实现这一目标，我们从基于阵列的系统中汲取灵感，并通过向后可达性在算法上解决安全问题。为了在我们丰富的环境中采用这种技术，我们利用了模型完成的模型理论机制，这令人惊讶地被证明是验证关系系统的有效工具，并且代表了本文的主要原创贡献。通过这种方式，我们追求双重目的。一方面，我们隔离了三个值得注意的类，它们的后向可达性终止，进而见证了可判定性。其中两个类与我们对文献中挑选出来的条件的处理方法有关，而第三个是真正新颖的。另一方面，我们能够在实现中利用 SMT 技术，在基于阵列的系统的著名 MCMT（Model Checker Modulo Theories）模型检查器的基础上进行扩展，并对其进行扩展，以使我们所有的基础成果都完全可操作。总而言之，目前的贡献深深植根于模型理论在计算机科学中应用的悠久传统。特别是，