# Decomposition theorems and model-checking for the modal μ-calculus

@article{Bojanczyk2014DecompositionTA,
title={Decomposition theorems and model-checking for the modal $\mu$-calculus},
author={Mikolaj Bojanczyk and Christoph Dittmann and Stephan Kreutzer},
journal={Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
year={2014}
}
• Published 9 May 2014
• Mathematics
• Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
We prove a general decomposition theorem for the modal μ-calculus Lμ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two substructures M1 and M2 plus edges from M1 to M2, then the formulas true at a node in M only depend on the formulas true in the respective substructures in a sense made precise below. As a consequence we show that the model-checking problem for Lμ is fixed-parameter…

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