We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems whose coordination between components share the same pattern, using inductive definitions similar to the ones used to describe algebraic data types or recursive data structures. Further, we give a verification method for the parametric systems described in this language, relying on the automatic synthesis of structural invariants that enable proving general safety properties (mutual exclusion, absence of deadlocks). The invariants are defined using the WSkS fragment of the monadic second order logic, known to be decidable by a classical automata-logic connection. This reduces the safety verification problem to checking satisfiability of a WSkS formula.

中文翻译：

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验证电感定义的参数化系统的安全特性

我们引入了术语代数作为一种新的形式规范语言，用于分布式系统的协调架构，由有限但无限数量的组件组成。该语言允许使用类似于用于描述代数数据类型或递归数据结构的归纳定义来描述无限组系统，这些系统的组件之间的协调共享相同的模式。此外，我们为用这种语言描述的参数系统提供了一种验证方法，依赖于结构不变量的自动合成，能够证明一般安全属性（互斥，没有死锁）。不变量是使用一元二阶逻辑的 WSkS 片段定义的，已知可以通过经典的自动机逻辑连接来判定。