Abstract
The \(\mu \)-calculus is an expressive propositional modal logic augmented with least and greatest fixed-points, and encompasses many temporal, program, dynamic and description logics. The model checking problem for the \(\mu \)-calculus is known to be in NP \(\cap \) Co-NP. In this paper, we study the model checking problem for the \(\mu \)-calculus extended with graded modalities. These constructors allow to express numerical constraints on the occurrence of accessible nodes (worlds) satisfying a certain formula. It is known that the model checking problem for the graded \(\mu \)-calculus with finite models is in EXPTIME. In the current work, we introduce a linear-time model checking algorithm for the graded \(\mu \)-calculus when models are finite unranked trees.
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Acknowledgment
This work was partially developed under the support of the Mexican National Science Council (CONACYT) in the scope of the Cátedras CONACYT project Infraestructura para Agilizar el Desarrollo de Sistemas Centrados en el Usuario (Ref 3053).
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Bárcenas, E., Benítez-Guerrero, E., Lavalle, J. (2015). On the Model Checking of the Graded \(\mu \)-calculus on Trees. In: Sidorov, G., Galicia-Haro, S. (eds) Advances in Artificial Intelligence and Soft Computing. MICAI 2015. Lecture Notes in Computer Science(), vol 9413. Springer, Cham. https://doi.org/10.1007/978-3-319-27060-9_14
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DOI: https://doi.org/10.1007/978-3-319-27060-9_14
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