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

Lange, Martin

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 177-190.

This paper analyses the complexity of model checking fixpoint logic with Chop - an extension of the modal $\mu$-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$\cap$co-UP. For any fragment of fixed alternation depth, in particular alternation- free formulas it is P-complete.

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