Abstract
Modal dependence logic (MDL) was introduced recently by Väänänen. It enhances the basic modal language by an operator = (·). For propositional variables p 1,…,p n the atomic formula = (p 1,…,p n − 1,p n ) intuitively states that the value of p n is determined solely by those of p 1,…,p n − 1.
We show that model checking for MDL formulae over Kripke structures is NP-complete and further consider fragments of MDL obtained by restricting the set of allowed propositional and modal connectives. It turns out that several fragments, e.g., the one without modalities or the one without propositional connectives, remain NP-complete.
We also consider the restriction of MDL where the length of each single dependence atom is bounded by a number that is fixed for the whole logic. We show that the model checking problem for this bounded MDL is still NP-complete. Furthermore we almost completely classifiy the computational complexity of the model checking problem for all restrictions of propositional and modal operators for both unbounded as well as bounded MDL.
An extended version of this article can be found on arXiv.org [3].
ACM Subject Classifiers: F.2.2 Complexity of proof procedures; F.4.1 Modal logic; D.2.4 Model checking.
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References
Beyersdorff, O., Meier, A., Mundhenk, M., Schneider, T., Thomas, M., Vollmer, H.: Model checking CTL is almost always inherently sequential. Logical Methods in Computer Science (2011), http://arxiv.org/abs/1103.4990v1
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)
Ebbing, J., Lohmann, P.: Complexity of model checking for modal dependence logic. CoRR abs/1104.1034v1 (2011), http://arxiv.org/abs/1104.1034v1
Hemaspaandra, E.: The complexity of poor man’s logic. CoRR cs.LO/9911014v2 (2005), http://arxiv.org/abs/cs/9911014v2
Hemaspaandra, E., Schnoor, H., Schnoor, I.: Generalized modal satisfiability. J. Comput. Syst. Sci. 76(7), 561–578 (2010)
Lewis, H.: Satisfiability problems for propositional calculi. Mathematical Systems Theory 13, 45–53 (1979)
Lohmann, P., Vollmer, H.: Complexity Results for Modal Dependence Logic. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 411–425. Springer, Heidelberg (2010), http://dx.doi.org/10.1007/978-3-642-15205-4_32
Sevenster, M.: Model-theoretic and computational properties of modal dependence logic. Journal of Logic and Computation 19(6), 1157–1173 (2009), http://logcom.oxfordjournals.org/cgi/content/abstract/exn102v1
Väänänen, J.: Dependence logic: A new approach to independence friendly logic. London Mathematical Society Student Texts, vol. 70. Cambridge University Press (2007)
Väänänen, J.: Modal dependence logic. In: Apt, K.R., van Rooij, R. (eds.) New Perspectives on Games and Interaction, Texts in Logic and Games, vol. 4, pp. 237–254. Amsterdam University Press (2008)
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Ebbing, J., Lohmann, P. (2012). Complexity of Model Checking for Modal Dependence Logic. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds) SOFSEM 2012: Theory and Practice of Computer Science. SOFSEM 2012. Lecture Notes in Computer Science, vol 7147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27660-6_19
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