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Realizing Omega-regular Hyperproperties
arXiv - CS - Logic in Computer Science Pub Date : 2021-01-18 , DOI: arxiv-2101.07161
Bernd Finkbeiner, Christopher Hahn, Jana Hofmann, Leander Tentrup

We studied the hyperlogic HyperQPTL, which combines the concepts of trace relations and $\omega$-regularity. We showed that HyperQPTL is very expressive, it can express properties like promptness, bounded waiting for a grant, epistemic properties, and, in particular, any $\omega$-regular property. Those properties are not expressible in previously studied hyperlogics like HyperLTL. At the same time, we argued that the expressiveness of HyperQPTL is optimal in a sense that a more expressive logic for $\omega$-regular hyperproperties would have an undecidable model checking problem. We furthermore studied the realizability problem of HyperQPTL. We showed that realizability is decidable for HyperQPTL fragments that contain properties like promptness. But still, in contrast to the satisfiability problem, propositional quantification does make the realizability problem of hyperlogics harder. More specifically, the HyperQPTL fragment of formulas with a universal-existential propositional quantifier alternation followed by a single trace quantifier is undecidable in general, even though the projection of the fragment to HyperLTL has a decidable realizability problem. Lastly, we implemented the bounded synthesis problem for HyperQPTL in the prototype tool BoSy. Using BoSy with HyperQPTL specifications, we have been able to synthesize several resource arbiters. The synthesis problem of non-linear-time hyperlogics is still open. For example, it is not yet known how to synthesize systems from specifications given in branching-time hyperlogics like HyperCTL$^*$.

中文翻译:

实现欧米茄常规超性能

我们研究了超级逻辑HyperQPTL,它结合了跟踪关系和$ \ omega $ -regularity的概念。我们证明了HyperQPTL具有很高的表达力,它可以表达一些特性,例如及时性,有界等待资助,认知特性,尤其是任何$ \ omega $-常规特性。这些属性在先前研究的Hyperlogic(例如HyperLTL)中无法表达。同时,我们认为从某种意义上说,HyperQPTL的表现力是最佳的,对于$ \ omega $-常规超属性而言,更具表现力的逻辑将具有无法确定的模型检查问题。我们还研究了HyperQPTL的可实现性问题。我们表明,对于包含诸如及时性之类的属性的HyperQPTL片段,可实现性是可决定的。但是,与可满足性问题相反,命题量化确实使超级逻辑学的可实现性问题更加困难。更具体地说,具有通用-普遍性命题量词替换符的公式的HyperQPTL片段后面紧跟一个跟踪量词通常是无法确定的,即使将片段投影到HyperLTL上也存在可确定的可实现性问题。最后,我们在原型工具BoSy中实现了HyperQPTL的有界综合问题。通过将BoSy与HyperQPTL规范配合使用,我们已经能够合成多个资源仲裁器。非线性时间超级逻辑学的综合问题仍然存在。例如,尚不知道如何根据分支时间超级逻辑(如HyperCTL $ ^ * $)中给出的规范来合成系统。通常,无法确定具有通用存在的命题量词替换符且后接单个跟踪量词的HyperQPTL公式片段,即使将片段投影到HyperLTL上也存在可确定的可实现性问题。最后,我们在原型工具BoSy中实现了HyperQPTL的有界综合问题。通过将BoSy与HyperQPTL规范配合使用,我们已经能够合成多个资源仲裁器。非线性时间超级逻辑学的综合问题仍然存在。例如,尚不知道如何根据分支时间超级逻辑(如HyperCTL $ ^ * $)中给出的规范来合成系统。通常,无法确定具有通用存在的命题量词替换符的公式的HyperQPTL片段,然后是单个跟踪量词,即使将片段投影到HyperLTL时也存在可确定的可实现性问题。最后,我们在原型工具BoSy中实现了HyperQPTL的有界综合问题。通过将BoSy与HyperQPTL规范配合使用,我们已经能够合成多个资源仲裁器。非线性时间超级逻辑学的综合问题仍然存在。例如,尚不知道如何根据分支时间超级逻辑(如HyperCTL $ ^ * $)中给出的规范来合成系统。即使将片段投影到HyperLTL都有可确定的可实现性问题。最后,我们在原型工具BoSy中实现了HyperQPTL的有界综合问题。通过将BoSy与HyperQPTL规范配合使用,我们已经能够合成多个资源仲裁器。非线性时间超级逻辑学的综合问题仍然存在。例如,尚不知道如何根据分支时间超级逻辑(如HyperCTL $ ^ * $)中给出的规范来合成系统。即使将片段投影到HyperLTL都有可确定的可实现性问题。最后,我们在原型工具BoSy中实现了HyperQPTL的有界综合问题。通过将BoSy与HyperQPTL规范配合使用,我们已经能够合成多个资源仲裁器。非线性时间超级逻辑学的综合问题仍然存在。例如,尚不知道如何根据分支时间超级逻辑(如HyperCTL $ ^ * $)中给出的规范来合成系统。
更新日期:2021-01-19
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