Hyperproperties have received increasing attention in the last decade due to their importance e.g. for security analyses. Past approaches have focussed on synchronous analyses, i.e. techniques in which different paths are compared lockstepwise. In this paper, we systematically study asynchronous analyses for hyperproperties by introducing both a novel automata model (Alternating Asynchronous Parity Automata) and the temporal fixpoint calculus $\Hmu$, the first fixpoint calculus that can systematically express hyperproperties in an asynchronous manner and at the same time subsumes the existing logic HyperLTL. We show that the expressive power of both models coincides over fixed path assignments. The high expressive power of both models is evidenced by the fact that decision problems of interest are highly undecidable, i.e. not even arithmetical. As a remedy, we propose approximative analyses for both models that also induce natural decidable fragments.

中文翻译：

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异步超属性的自动机和固定点

超属性在过去十年中受到越来越多的关注，因为它们非常重要，例如用于安全分析。过去的方法侧重于同步分析，即同步比较不同路径的技术。在本文中，我们通过引入新的自动机模型（交替异步奇偶校验自动机）和时间定点演算 $\Hmu$，系统地研究超属性的异步分析，这是第一个可以以异步方式系统地表达超属性的定点演算。同时包含了现有的逻辑 HyperLTL。我们表明两种模型的表达能力在固定路径分配上是一致的。感兴趣的决策问题是高度不可判定的，即甚至不是算术问题，这证明了这两种模型的高表达能力。