Update and abstraction in model checking of knowledge and branching time

We present (update+abstraction) algorithm for model checking a fusion of Computation Tree Logic and Propositional Logic of Knowledge in systems with the perfect recall synchronous semantics. It has been already known that the problem is decidable with a non-elementary lower bound. The decidability follows from interpretation of the problem in a so-called Chain Logic and then in the Second Order Logic of Monadic Successors. This time we give a direct algorithm for model checking and detailed time upper bound where a number of different parameters are taken into count (i.e. a number of agents, a number of states, knowledge depth, formula size). We present a toy experiment with this algorithm that encourages our hope that the algorithm can be used in practice.