Three notes on the complexity of model checking fixpoint logic with chop

This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations to derive the following results: the combined model checking complexity as well as the data complexity of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression complexity of FLC is trivially P-hard and limited from above by the complexity of solving a parity game, i.e. in UP ∩ co-UP. For any fragment of fixed alternation depth, in particular alternation- free formulas it is P-complete