UNITY is a model for concurrent specifications with a complete logic for proving progress properties of the form “ P leads to Q ”. UNITY is generalized to U-specifications by giving more freedom to specify the steps that are to be taken infinitely often. In particular, these steps can correspond to non-total relations. The generalization keeps the logic sound and complete. The paper exploits the generalization in two ways. Firstly, the logic remains sound when the specification is extended with hypotheses of the form “ F leads to G ”. As the paper shows, this can make the logic incomplete. The generalization is used to show that the logic remains complete, if the added hypotheses “ F leads to G ” satisfy “ F unless G ”. The main result extends the applicability and completeness of UNITY logic to proofs that a given concurrent program satisfies any given formula of LTL, linear temporal logic, without the next-operator which is omitted because it is sensitive to stuttering. For this purpose, the program, written as a UNITY program, is extended with a number of boolean variables. The proof method relies on implementing the LTL formula, i.e., restricting the specification in such a way that only those runs remain that satisfy the formula. This result is a variation of the classical construction of a Büchi automatonfor a given LTL formula that accepts precisely those runs that satisfy the formula.

中文翻译：

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UNITY 和 Büchi 自动机

UNITY 是并发规范的模型，具有完整的逻辑来证明形式的进度属性磷造成问”。UNITY 通过给予更多自由来指定无限频繁地执行的步骤，从而被推广到 U 规范。特别是，这些步骤可以对应于非全关系。概括保持逻辑健全和完整。本文以两种方式利用泛化。首先，当规范扩展为“F造成G”。正如论文所示，这会使逻辑不完整。概括用于表明逻辑仍然完整，如果添加的假设“F造成G“满足”F除非G”。主要结果将 UNITY 逻辑的适用性和完整性扩展到证明给定的并发程序满足任何给定的 LTL 公式，线性时间逻辑，没有 next-operator，因为它对口吃敏感而被省略。为此，编写为 UNITY 程序的程序扩展了许多布尔变量。证明方法依赖于实现 LTL 公式，即以这样一种方式限制规范，即只有那些满足公式的运行仍然存在。这个结果是对给定 LTL 公式的 Büchi 自动机的经典构造的变体，该 LTL 公式精确地接受那些满足公式的运行。