On the complexity of reasoning about dynamic policies

  • Authors:

  • Stefan Göller

  • Affiliations:

  • Universität Stuttgart, FMI, Germany

  • Venue:
  • CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
  • Year:
  • 2007

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Abstract

We study the complexity of satisfiability for DLPdyn+, an expressive logic introduced by Demri that allows to reason about dynamic policies. DLPdyn+ extends the logic DLPdyn of Pucella and Weissman, which in turn extends van der Meyden's Dynamic Logic of Permission (DLP). DLPdyn+ generously enhances DLP and DLPdyn by allowing to update the policy set by adding or removing policy transitions, which are defined as a direct product of two sets, each specified by a formula of the logic itself. It is proven that satisfiability for DLPdyn+ is complete for deterministic exponential time. Our results close the complexity gap of satisfiability for DLPdyn+ from 2EXP, and for DLPdyn from NEXP, to EXP respectively, matching the EXP lower bound both inherit from Propositional Dynamic Logic (PDL). To prove the EXP upper bound for DLPdyn+, we first proceed by accurately identifying a suitable generalization of PDL, which allows to use compressed programs and then find a satisfiability preserving translation from DLPdyn+ to this extension of PDL. To finally show the EXP upper bound for DLPdyn+, we prove that satisfiability of our extension of PDL lies in EXP.