Enriched MU-Calculi Module Checking

The model checking problem for open systems has been intensively studied inthe literature, for both finite-state (module checking) and infinite-state(pushdown module checking) systems, with respect to Ctl and Ctl*. In thispaper, we further investigate this problem with respect to the \mu-calculusenriched with nominals and graded modalities (hybrid graded Mu-calculus), inboth the finite-state and infinite-state settings. Using an automata-theoreticapproach, we show that hybrid graded \mu-calculus module checking is solvablein exponential time, while hybrid graded \mu-calculus pushdown module checkingis solvable in double-exponential time. These results are also tight since theymatch the known lower bounds for Ctl. We also investigate the module checkingproblem with respect to the hybrid graded \mu-calculus enriched with inverseprograms (Fully enriched \mu-calculus): by showing a reduction from the dominoproblem, we show its undecidability. We conclude with a short overview of themodel checking problem for the Fully enriched Mu-calculus and the fragmentsobtained by dropping at least one of the additional constructs