Complexity of Model Checking for Modal Dependence Logic

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.