Decomposition theorems and model-checking for the modalμ-calculus

Mikolaj Bojanczyk, Christoph Dittmann, Stephan Kreutzer
2014 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) - CSL-LICS '14  
We prove a general decomposition theorem for the modal μ-calculus L_μ 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 M_1 and M_2 plus edges from M_1 to M_2, 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 L_μ is fixed-parameter
more » ... actable (fpt) on classes of structures of bounded Kelly-width or bounded DAG-width. As far as we are aware, these are the first fpt results for L_μ which do not follow from embedding into monadic second-order logic.
doi:10.1145/2603088.2603144 dblp:conf/csl/BojanczykDK14 fatcat:vfhrvywtezbvjis7i3mglnqzfq