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exptime-complete

RAIRO - Theoretical Informatics and Applications (1)

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Three notes on the complexity of model checking fixpoint logic with chop
Martin Lange
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 41 / Issue 2 / April 2007

Published online by Cambridge University Press:

18 July 2007, pp. 177-190

Print publication:

April 2007
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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.