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Unifying Hyper and Epistemic Temporal Logics

  • Laura Bozzelli
  • Bastien Maubert
  • Sophie Pinchinat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)

Abstract

In the literature, two powerful temporal logic formalisms have been proposed for expressing information-flow security requirements, that in general, go beyond regular properties. One is classic, based on the knowledge modalities of epistemic logic. The other one, the so-called hyper logic, is more recent and subsumes many proposals from the literature. In an attempt to better understand how these logics compare with each other, we consider the logic \(\text{\sffamily KCTL$^{*}$}\) (the extension of \(\text{\sffamily CTL$^{*}$}\) with knowledge modalities and synchronous perfect recall semantics) and \(\text{\sffamily HyperCTL$^{*}$}\). We first establish that \(\text{\sffamily KCTL$^{*}$}\) and \(\text{\sffamily HyperCTL$^{*}$}\) are expressively incomparable. Then, we introduce a natural linear past extension of \(\text{\sffamily HyperCTL$^{*}$}\), called \(\text{\sffamily HyperCTL$^{*}_{lp}$}\), that unifies \(\text{\sffamily KCTL$^{*}$}\) and \(\text{\sffamily HyperCTL$^{*}$}\). We show that the model-checking problem for \(\text{\sffamily HyperCTL$^{*}_{lp}$}\) is decidable, and we provide its exact computational complexity in terms of a new measure of path quantifiers’ alternation. For this, we settle open complexity issues for unrestricted quantified propositional temporal logic.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Laura Bozzelli
    • 1
  • Bastien Maubert
    • 2
  • Sophie Pinchinat
    • 3
  1. 1.UPMMadridSpain
  2. 2.LORIA - CNRSUniversité de LorraineNancyFrance
  3. 3.IRISAUniversité de Rennes 1RennesFrance

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