Open pNets are formal models that can express the behaviour of open systems, either synchronous, asynchronous, or heterogeneous. They are endowed with a symbolic operational semantics in terms of open automata, which allows us to check properties of such systems in a compositional manner. We present an algorithm computing these semantics, building predicates expressing the synchronisation conditions between the events of pNet sub-systems. Checking such predicates requires symbolic reasoning about first order logics and application-specific data. We use the Z3 SMT engine to check satisfiability of the predicates. We also propose and implement an optimised algorithm that performs part of the pruning on the fly, and show its correctness with respect to the original one. We illustrate the approach using two use-cases: the first one is a classical process-algebra operator for which we provide several encodings, and prove some basic properties. The second one is industry-oriented and based on the so-called “BIP architectures”, which have been used to specify the control software of a nanosatellite at the EPFL Space Engineering Center. We use pNets to encode a BIP architecture extended with explicit data, compute its semantics and discuss its properties, and then show how our algorithms scale up, using a composition of two such architectures.

中文翻译：

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基于 SMT 的符号自动机生成

开放 pNet 是可以表达开放系统行为的正式模型，无论是同步的、异步的还是异构的。它们被赋予开放自动机方面的符号操作语义，这使我们能够以组合方式检查此类系统的属性。我们提出了一种计算这些语义的算法，构建表达 pNet 子系统事件之间同步条件的谓词。检查此类谓词需要对一阶逻辑和特定于应用程序的数据进行符号推理。我们使用 Z3 SMT 引擎来检查谓词的可满足性。我们还提出并实现了一种优化算法，该算法即时执行部分剪枝，并显示其相对于原始算法的正确性。我们使用两个用例来说明该方法：第一个是经典的过程代数算子，我们为其提供了几种编码，并证明了一些基本属性。第二种是面向行业的，基于所谓的“BIP 架构”，该架构已被用于指定 EPFL 空间工程中心的纳米卫星控制软件。我们使用 pNet 来编码一个用显式数据扩展的 BIP 架构，计算其语义并讨论其属性，然后展示我们的算法如何使用两个此类架构的组合进行扩展。