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A Remark on the Expressivity of Asynchronous TeamLTL and HyperLTL

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Foundations of Information and Knowledge Systems (FoIKS 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14589))

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Abstract

Linear temporal logic (LTL) is used in system verification to write formal specifications for reactive systems. However, some relevant properties, e.g. non-inference in information flow security, cannot be expressed in LTL. A class of such properties that has recently received ample attention is known as hyperproperties. There are two major streams in the research regarding capturing hyperproperties, namely hyperlogics, which extend LTL with trace quantifiers (HyperLTL), and logics that employ team semantics, extending truth to sets of traces. In this article we explore the relation between asynchronous LTL under set-based team semantics (TeamLTL) and HyperLTL. In particular we consider the extensions of TeamLTL with the Boolean disjunction and a fragment of the extension of TeamLTL with the Boolean negation, where the negation cannot occur in the left-hand side of the Until-operator or within the Global-operator. We show that TeamLTL extended with the Boolean disjunction is equi-expressive with the positive Boolean closure of HyperLTL restricted to one universal quantifier, while the left-downward closed fragment of TeamLTL extended with the Boolean negation is expressively equivalent with the Boolean closure of HyperLTL restricted to one universal quantifier.

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Acknowledgements

This work was supported by the Academy of Finland grant 345634 and the DFG grant VI 1045/1-1.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Juha Kontinen, Max Sandström & Jonni Virtema

  2. Department of Computer Science, University of Sheffield, Sheffield, UK

    Max Sandström & Jonni Virtema

Authors
  1. Juha Kontinen
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  2. Max Sandström
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  3. Jonni Virtema
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Corresponding author

Correspondence to Max Sandström .

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Editors and Affiliations

  1. Leibniz University Hannover, Hanover, Germany

    Arne Meier

  2. TU Wien, Wien, Austria

    Magdalena Ortiz

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Kontinen, J., Sandström, M., Virtema, J. (2024). A Remark on the Expressivity of Asynchronous TeamLTL and HyperLTL. In: Meier, A., Ortiz, M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2024. Lecture Notes in Computer Science, vol 14589. Springer, Cham. https://doi.org/10.1007/978-3-031-56940-1_15

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  • DOI: https://doi.org/10.1007/978-3-031-56940-1_15

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