Complexity of model checking for modal dependence logic

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. © 2012 Springer-Verlag.