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Linear-time Temporal Logic with Team Semantics: Expressivity and Complexity
arXiv - CS - Computational Complexity Pub Date : 2020-10-07 , DOI: arxiv-2010.03311
Jonni Virtema, Jana Hofmann, Bernd Finkbeiner, Juha Kontinen, and Fan Yang

We study the expressivity and the model checking problem of linear temporal logic with team semantics (TeamLTL). In contrast to LTL, TeamLTL is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. Logics for hyperproperties have so far been mostly obtained by extending temporal logics like LTL and QPTL with trace quantification, resulting in HyperLTL and HyperQPTL. We study the expressiveness of TeamLTL (and its extensions with downward closed generalised atoms A and connectives such as Boolean disjunction v) in comparison to HyperLTL and HyperQPTL. Thereby, we also obtain a number of model checking results for TeamLTL, a question which is so far an open problem. The two types of logics follow a fundamentally different approach to hyperproperties and are are of incomparable expressiveness. We establish that the universally quantified fragment of HyperLTL subsumes the so-called k-coherent fragment of TeamLTL(A,v). This also implies that the model checking problem is decidable for the fragment. We show decidability of model checking of the so-called "left-flat" fragment of TeamLTL(A,v) via a translation to a decidable fragment of HyperQPTL. Finally, we show that the model checking problem of TeamLTL with Boolean disjunction and inclusion atom is undecidable.

中文翻译:

具有团队语义的线性时间时序逻辑:表现力和复杂性

我们研究了具有团队语义的线性时间逻辑(TeamLTL)的表达性和模型检查问题。与 LTL 相比,TeamLTL 能够定义超属性,即与多个执行跟踪相关的属性。迄今为止,超属性的逻辑主要是通过扩展 LTL 和 QPTL 等具有跟踪量化的时间逻辑获得的,从而产生 HyperLTL 和 HyperQPTL。与 HyperLTL 和 HyperQPTL 相比,我们研究了 TeamLTL(及其具有向下闭合的广义原子 A 和连接词,如布尔析取 v)的表达能力。从而,我们还获得了许多 TeamLTL 的模型检查结果,这是一个迄今为止尚未解决的问题。这两种逻辑对超属性采用了根本不同的方法,并且具有无与伦比的表现力。我们确定 HyperLTL 的通用量化片段包含 TeamLTL(A,v) 的所谓 k 相干片段。这也意味着模型检查问题对于片段是可判定的。我们通过转换为 HyperQPTL 的可判定片段,展示了 TeamLTL(A,v) 的所谓“左平”片段的模型检查的可判定性。最后,我们证明了具有布尔析取和包含原子的 TeamLTL 模型检查问题是不可判定的。
更新日期:2020-10-08
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