Three notes on the complexity of model checking fixpoint logic with chop
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 177-190.

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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.

DOI : 10.1051/ita:2007011
Classification : 03B44, 68Q17, 68Q60
Mots-clés : model checking, games, EXPTIME-complete 
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     author = {Lange, Martin},
     title = {Three notes on the complexity of model checking fixpoint logic with chop},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {177--190},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {2},
     year = {2007},
     doi = {10.1051/ita:2007011},
     zbl = {1133.68046},
     mrnumber = {2350643},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007011/}
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Lange, Martin. Three notes on the complexity of model checking fixpoint logic with chop. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 177-190. doi : 10.1051/ita:2007011. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007011/

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