Abstract
We study the complexity of satisfiability for DLP\(_{\mathrm{dyn}}^+\), an expressive logic introduced by Demri that allows to reason about dynamic policies. DLP\(_{\mathrm{dyn}}^+\) extends the logic DLPdyn of Pucella and Weissman, which in turn extends van der Meyden’s Dynamic Logic of Permission (DLP). DLP\(_{\mathrm{dyn}}^+\) 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\(_{\mathrm{dyn}}^+\) is complete for deterministic exponential time. Our results close the complexity gap of satisfiability for DLP\(_{\mathrm{dyn}}^+\) 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\(_{\mathrm{dyn}}^+\), 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\(_{\mathrm{dyn}}^+\) to this extension of PDL. To finally show the EXP upper bound for DLP\(_{\mathrm{dyn}}^+\), we prove that satisfiability of our extension of PDL lies in EXP!.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the Association for Computing Machinery 28(1), 114–133 (1981)
Danecki, R.: Nondeterministic Propositional Dynamic Logic with Intersection is decidable. In: Skowron, A. (ed.) Computation Theory. LNCS, vol. 208, pp. 34–53. Springer, Heidelberg (1985)
Demri, S.: A reduction from DLP to PDL. Journal of Logic and Computation 15(5), 767–785 (2005)
Fischer, M.J., Ladner, R.E.: Propositional Dynamic Logic of Regular Programs. Journal of Computer and System Sciences 18(2), 194–211 (1979)
Göller, S., Lohrey, M., Lutz, C.: PDL with Intersection and Converse is 2EXP-Complete. In: Proc. of FoSSaCS 2007, vol. 4423, pp. 198–212. Springer, Heidelberg (2007)
Lange, M., Lutz, C.: 2-ExpTime Lower Bounds for Propositional Dynamic Logics with Intersection. Journal of Symbolic Logic 70(4), 1072–1086 (2005)
Löding, C., Rohde, P.: Model Checking and Satisfiability for Sabotage Modal Logic. In: Pandya, P.K., Radhakrishnan, J. (eds.) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. LNCS, vol. 2914, pp. 302–313. Springer, Heidelberg (2003)
Lutz, C., Walther, D.: PDL with Negation of Atomic Programs. Journal of Applied Non-Classical Logic 15(2), 189–214 (2005)
Pratt, V.R.: A Practical Decision Method for Propositional Dynamic Logic: Preliminary Report. In: Proc. of STOC 1980, pp. 326–337. ACM Press, New York (1978)
Pucella, R., Weissman, V.: Reasoning about Dynamic Policies. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 453–467. Springer, Heidelberg (2004)
van Benthem, J.: An Essay on Sabotage and Obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005)
van der Meyden, R.: The Dynamic Logic of Permission. Journal of Logic and Computation 6(3), 465–479 (1996)
Vardi, M.Y.: Reasoning about the Past with Two-Way Automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)
Vardi, M.Y., Wolper, P.: Automata-Theoretic Techniques for Modal Logics of Programs. Journal of Computer and System Sciences 32(2), 183–221 (1986)
Wieringa, R.J., Meyer, J.-J.C.: Applications of Deontic Logic in Computer Science: A Concise Overview. In: Deontic Logic in Computer Science, pp. 17–40 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Göller, S. (2007). On the Complexity of Reasoning About Dynamic Policies. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-74915-8_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74914-1
Online ISBN: 978-3-540-74915-8
eBook Packages: Computer ScienceComputer Science (R0)