Model checking for hybrid branching-time logics

Abstract

We consider hybridisations of the full branching time logic CTL⁎ and its prominent fragments CTL, CTL+ and FCTL+ through the addition of nominals, binders and jumps. We formally define three types of hybridisations by restricting the interplay between hybrid operators and path formulas contrary to previous proposals in the literature which ignored potential problems with a formal semantics. We then investigate the model checking problem for these logics obtaining expression complexities from PSpace -completeness to non-elementary decidability and data complexities ranging from NLogSpace to PSpace. Lastly, we identify a family of fragments of these hybrid logics, called the bounded fragments, that (in some cases) have the same model checking complexity as their non-hybrid counterparts.