Model checking is a technique which is being used successfully in automatic program. More than 25 years of research on model checking has brought forward various techniques and tricks which can handle complex tasks or just massive structures as caused by the state-space explosion problem for instance.Mathematically, the model checking problem is to determine whether or not a given relational structure is a model of a given formula, typically of a temporal logic. In the domain of program verification, very weak temporal logics suffice in order to express relevant properties. Temporal logics of higher expressive power can naturally express more complex properties. In particular, there already are logics which can express all kinds of decision problems in the range of NP andabove.In this project we will investigate the use of advanced model checking techniques for the solving of decision and computation problems in all kinds of diverse areas like bio-informatics, database querying, network routing, computational linguistics, etc. We will, for example, identify important problems in this area, encode them as model checking problems in logics of suitable expressive power, and use partial evaluation, manual optimisations, and the vast toolbox of model checking specialisations in order to obtain new and competitive algorithms for and insights into such problems. We will design suitable temporal logics where there are none, and build model checking algorithms which serve as a generic starting point for the solving of such problems.