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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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References

  1. Baumeister, J., Coenen, N., Bonakdarpour, B., Finkbeiner, B., Sanchez, C.: A Temporal logic for asynchronous hyperproperties. In: Silva, A., Leino, K.R.M. (eds.) Computer Aided Verification. CAV 2021. LNCS, vol. 12759, pp. 694–717. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81685-8_33

  2. Clarkson, M.R., Finkbeiner, B., Koleini, M., Micinski, K.K., Rabe, M.N., Sánchez, C.: Temporal logics for hyperproperties. In: Abadi, M., Kremer, S. (eds.) Principles of Security and Trust. POST 2014. LNCS, vol. 8414, pp. 265–284. Springer, Berlin, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54792-8_15

  3. Clarkson, M.R., Schneider, F.B.: Hyperproperties. J. Comput. Secur. 18(6), 1157–1210 (2010)

    Article  Google Scholar 

  4. Coenen, N., Finkbeiner, B., Hahn, C., Hofmann, J.: The hierarchy of hyperlogics. In: LICS 2019, pp. 1–13. IEEE (2019)

    Google Scholar 

  5. Finkbeiner, B.: Temporal hyperproperties. Bull. EATCS (123) (2017). http://eatcs.org/beatcs/index.php/beatcs/article/view/514

  6. Finkbeiner, B., Hahn, C., Lukert, P., Stenger, M., Tentrup, L.: Synthesis from hyperproperties. Acta Informatica 57(1–2), 137–163 (2020). https://doi.org/10.1007/s00236-019-00358-2

    Article  MathSciNet  Google Scholar 

  7. Finkbeiner, B., Zimmermann, M.: The first-order logic of hyperproperties. In: Vollmer, H., Vallée, B. (eds.), STACS 2017, volume 66 of LIPIcs, pp. 30:1–30:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

    Google Scholar 

  8. Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: On the temporal analysis of fairness. In: Abrahams, P.W., Lipton, R.J., Bourne, S.R. (eds.), Conference Record of the Seventh Annual ACM Symposium on Principles of Programming Languages, Las Vegas, Nevada, USA, January 1980, pp. 163–173. ACM Press (1980). https://doi.org/10.1145/567446.567462

  9. Gutsfeld, J.O., Meier, A., Ohrem, C., Virtema, J.: Temporal team semantics revisited. In: Baier, C., Fisman, D. (eds.), LICS ’22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science, Haifa, Israel, 2–5 August 2022, pp. 44:1–44:13. ACM (2022). https://doi.org/10.1145/3531130.3533360

  10. Gutsfeld, J.O., Muller-Olm, M., Ohrem, C.: Automata and fixpoints for asynchronous hyperproperties. Proc. ACM Program. Lang. 5(POPL), 1–29 (2021). https://doi.org/10.1145/3434319

  11. Kontinen, J., Sandström, M.: On the expressive power of TeamLTL and first-order team logic over hyperproperties. In: Silva, A., Wassermann, R., de Queiroz, R. (eds.) WoLLIC 2021. LNCS, vol. 13038, pp. 302–318. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88853-4_19

    Chapter  Google Scholar 

  12. Kontinen, J., Sandstrom, M., Virtema, J.: Set semantics for asynchronous teamltl: expressivity and complexity. In: Leroux, J ., Lombardy, S., Peleg, D. (eds.), 48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023, August 28 to 1 September 2023, Bordeaux, France, volume 272 of LIPIcs, pp. 60:1–60:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023). https://doi.org/10.4230/LIPIcs.MFCS.2023.60

  13. Krebs, A., Meier, A., Virtema, J.: A team based variant of CTL. In: Grandi, F., Lange, M., Lomuscio, A. (eds.), 22nd International Symposium on Temporal Representation and Reasoning, TIME 2015, Kassel, Germany, 23–25 September 2015, pp. 140–149. IEEE Computer Society (2015). https://doi.org/10.1109/TIME.2015.11

  14. Krebs, A., Meier, A., Virtema, J., Zimmermann, M.: Team semantics for the specification and verification of hyperproperties. In: Potapov, I., Spirakis, P., Worrell, J. (eds.), MFCS 2018, vol. 117, pp. 10:1–10:16, Dagstuhl, Germany. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018)

    Google Scholar 

  15. McLean, J.: Proving noninterference and functional correctness using traces. J. Comput. Secur. 1(1), 37–58 (1992). https://doi.org/10.3233/JCS-1992-1103

    Article  Google Scholar 

  16. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE Computer Society (1977)

    Google Scholar 

  17. Rabe, M.N.: A Temporal Logic Approach to Information-Flow Control. PhD thesis, Saarland University (2016)

    Google Scholar 

  18. Roscoe, A.W.: CSP and determinism in security modelling. In: Proceedings of the 1995 IEEE Symposium on Security and Privacy, Oakland, California, USA, 8–10 May 1995, pp. 114–127. IEEE Computer Society (1995). https://doi.org/10.1109/SECPRI.1995.398927

  19. Väänänen, J.: Dependence Logic. Cambridge University Press (2007)

    Google Scholar 

  20. Virtema, J., Hofmann, J., Finkbeiner, B., Kontinen, J., Yang, F.: Linear-time temporal logic with team semantics: expressivity and complexity. In: Bojanczyk, M., Chekuri, C. (eds.), 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2021, 15–17 December 2021, Virtual Conference, volume 213 of LIPIcs, pp. 52:1–52:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.FSTTCS.2021.52

  21. Zdancewic, S., Myers, A.C.: Observational determinism for concurrent program security. In: 16th IEEE Computer Security Foundations Workshop (CSFW-16 2003), 30 June–2 July 2003, Pacific Grove, CA, USA, p. 29. IEEE Computer Society (2003). https://doi.org/10.1109/CSFW.2003.1212703

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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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