On the Complexity of Reasoning About Dynamic Policies

We study the complexity of satisfiability for DLP+dyn , an expressive logic introduced by Demri that allows to reason about dynamic policies. DLP+dyn extends the logic DLPdyn of Pucella and Weissman, which in turn extends van der Meyden’s Dynamic Logic of Permission (DLP). DLP+dyn 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 DLP+dyn is complete for deterministic exponential time. Our results close the complexity gap of satisfiability for DLP+dyn 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 DLP+dyn, 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 DLP+dyn to this extension of PDL. To finally show the EXP upper bound for DLP+dyn , we prove that satisfiability of our extension of PDL lies in EXP .