Parameterized Complexity of Dynamic Belief Updates: A Complete Map

Dynamic Belief Update is a model checking problem in Dynamic Epistemic Logic concerning the effect of applying a number of epistemic actions on an initial epistemic model. It can also be considered as a plan verification problem in epistemic planning. The problem is known to be PSPACE-hard. To better understand the source of complexity of the problem, previous research has investigated the complexity of 128 parameterized versions of the problem with parameters such as number of agents and size of epistemic actions. The complexity of many parameter combinations has been determined, but previous research left 14 parameter combinations open. In this paper, we solve all of these open problems. Most of the parameter combinations turns out to be fixed-parameter intractable, except for 2 that are fixed-parameter tractable.