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Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity

Authors Jonni Virtema , Jana Hofmann , Bernd Finkbeiner , Juha Kontinen , Fan Yang

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Author Details

Jonni Virtema
  • Institute for Theoretical Computer Science, Leibniz Universität Hannover, Germany
  • Department of Computer Science, University of Sheffield, UK
Jana Hofmann
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Bernd Finkbeiner
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Juha Kontinen
  • Department of Mathematics and Statistics, University of Helsinki, Finland
Fan Yang
  • Department of Mathematics and Statistics, University of Helsinki, Finland

Funding

Jana Hofmann and Bernd Finkbeiner: Partially supported by the German Research Foundation (DFG) as part of the Collaborative Research Center "Foundations of Perspicuous Software Systems" (TRR 248, 389792660) and by the European Research Council (ERC) Grant OSARES (No. 683300).
  • Virtema, Jonni: Supported by the DFG grant VI 1045/1-1.
  • Kontinen, Juha: Supported by grant 308712 of the Academy of Finland.
  • Yang, Fan: Supported by grants 330525 and 308712 of Academy of Finland, and Research Funds of University of Helsinki.

Cite As Get BibTex

Jonni Virtema, Jana Hofmann, Bernd Finkbeiner, Juha Kontinen, and Fan Yang. Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.FSTTCS.2021.52

Abstract

We study the expressivity and complexity of model checking of linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking results for TeamLTL and identify its undecidability frontier. In particular, we show decidability of model checking of the so-called left-flat fragment of any downward closed TeamLTL -extension. Moreover, we establish that the model checking problem of TeamLTL with Boolean disjunction and inclusion atoms is undecidable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Modal and temporal logics
Keywords
  • Linear temporal logic
  • Hyperproperties
  • Model Checking
  • Expressivity

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