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Abstract: The model checking problem for open systems has been intensively studied inthe literature, for both finite-state module checking and infinite-statepushdown 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.



Author: Alessandro Ferrante, Aniello Murano, Mimmo Parente

Source: https://arxiv.org/



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